John  3wett 


3  fi 


» 


Plate  I 


A  TEXT-BOOK! 


ELEMENTS  OF  PHYSICS 


HIGH  SCHOOLS  AND  ACADEMIES, 


BY 

ALFRED   P.  GAGE,  A.M., 

INSTRUCTOR  IN  PHYSICS  IN  THE  ENGLISH  HIGH  SCHOOL,  BOSTON,   MASS. 


BOSTON: 

PUBLISHED  BY  GINN  &  COMPANY. 
1888. 


33 


Entered  according  to  Act  of  Congress,  in  the  year  1882,  by 

ALFRED  P.  GAGE, 
in  the  Office  of  the  Librarian  of  Congress,  at  Washington. 

EDUCATION 


TYPOGRAPHY  BY  J.  8.  GUSHING  &  Co.,  BOSTON. 


PRESSWOKK  BY  GINN  &  Co.,  BOSTON. 


AUTHORS    PEEFAGE. 


IN  his  Report  for  the  year  1881,  Mr.  E.  P.  Seaver,  Superintendent 
of  the  Public  Schools  of  Boston,  says :  — 

"  It  is  a  cardinal  principle  in  modern  pedagogy  that  the  mind 
gains  a  real  and  adequate  knowledge  of  things  only  in  the  presence 
of  the  things  themselves.  Hence  the  first  step  in  all  good  teaching 
is  an  appeal  to  the  observing  powers.  The  objects  studied  and  the 
studying  mind  are  placed  in  the  most  direct  relations  with  one 
another  that  circumstances  admit.  Words  and  other  symbols  are 
not  allowed  to  intervene,  tempting  the  learner  to  satisfy  his  mind 
-rfith  ideas  obtained  at  second-hand.  One  application  of  this  prin- 
ciple is  seen  in  the  so-called  object-teaching;  but  the  principle  is 
applicable  to  all  teaching,  and  all  methods  of  teaching  based  on 
it  are  known  as  objective  methods.  The  theory  goes  even  further, 
and  declares,  in  general,  that  no  teaching  which  is  not  objective  in 
method  can  properly  be  called  teaching  at  all.  Hence  we  have  this 
test :  Is  our  teaching  objective  in  method  ?  " 

This  unequivocal  language,  from  the  pen  of  one  of  our  foremost 
educators,  faithfully  and  forcibly  reflects  the  sentiment  of  the  age, 
and  leaves  nothing  further  that  need  be  said  in  advocacy  of  object 
or  inductive  teaching.  The  question  for  us  to  consider  is,  How  shall 
object-teaching  be  conducted?  Shall  the  teacher  manipulate  the 
apparatus,  and  the  pupil  act  the  part  of  an  admiring  spectator? 
or,  Shall  the  pupil  be  supplied  with  such  apparatus  as  he  cannot 
conveniently  construct,  always  of  the  simplest  and  least  expensive 
kind,  with  which  he  shall  be  required,  under  the  guidance  of  his 
teacher,  to  interrogate  Nature  with  his  own  hands?  By  which 

5-i?  ?88 


IV 


wLU/hei  ^(hiH-e  the  most  vigorous  growth,  and  be  most 
likely  to  catch  something,  of  the  spirit  which  animates  and  encourages 
ike'  ;faitbi*ul  'myestfgak>E.?.'  Can  elegantly  illustrated  works  and  lucid 
lectures  on  anatomy  and  operative  surgery  take  the  place  of  the 
dissecting  room?  Have  lecture-room  displays  proved  very  effectual 
in  awakening  thought  and  in  kindling  fires  of  enthusiasm  in  the 
young?  Or  would  a  majority  of  our  practical  scientists  date  their 
first  inspiration  from  more  humble  beginnings,  with  such  rude  uten- 
sils, for  instance,  as  the  kitchen  affords?  Is  the  efficiency  of  instruc- 
tion in  the  natural  sciences  to  be  estimated  by  the  amount  of  costly 
apparatus  kept  on  show  in  glass  cases,  labelled  "  hands  off,"  or  by 
its  rude  pine  tables  and  crude  apparatus  bearing  the  scars,  scratches, 
and  other  marks  of  use  ?  Why  should  this  fundamental  study,  which 
logically  precedes  all  other  experimental  sciences,  and  ought  there- 
fore, beyond  all  others,  to  be  sound  and  thorough,  be  left  in  the 
condition  of  "a  mere  cram  subject"? 

Fortunately  we  are  able  to  appeal  to  experience  in  a  kindred 
field  for  an  answer  to  the  first  two  questions  propounded.  During 
the  last  twenty  years  there  has  been  almost  a  universal  change 
from  the  former  method  of  instruction  in  Chemistry  to  the  latter, 
so  that  to-day  our  best  high  schools  and  academies  are  provided 
with  chemical  laboratories  for  pupils'  work.  The  result  has  been 
that  this  branch,  which  was  formerly  a  dull  and  almost  profitless 
study,  has  become  one  of  the  most  interesting  and  useful  in  the  high 
school  curriculum.  Is  there  any  reason  why  laboratory  practice  should 
not  do  a  similar  work  for  Physics  ?  In  other  words,  Do  not  the  same 
arguments  that  have  been  urged  for  the  introduction  of  chemical 
laboratories  apply  with  equal  propriety  and  force  in  advocacy  of 
physical  laboratories? 

But  it  is  claimed  by  some  that  "  In  Physics  the  laboratory  practice 
must  necessarily  be  somewhat  limited,"  and  the  usual,  and  almost 
the  only  reason  given,  is  "on  account  of  the  expense."  This  objec- 
tion rests  upon  the  flimsiest  of  foundations.  The  expense  of 


equipping  and  maintaining  a  physical  laboratory  which  will  answer 
the  requirements  of  this  book,  ought  to  be  considerably  less  than 
a  similar  expense  to  meet  the  demands  of  Eliot  and  Storer's  Ele- 
mentary Manual  of  Chemistry.  In  the  English  High  School,  in  the 
city  of  Boston,  the  sum  of  three  hundred  dollars  has  furnished  a 
physical  laboratory  which  answers  the  requirements  of  a  large 
school.  Many  and  many  a  school  has  invested  in  showy  but  almost 
useless  apparatus,  —  for  example,  in  trifling  electric  playthings,  —  a 
sum  of  money  which  would  go  far  towards  the  establishment  of  a 
simple  working  laboratory.  But  more,  much  more,  depends  upon 
the  teacher  than  the  cost  of  material.  "  If  he  has  the  real  scientific 
spirit,  he  will  do  a  great  deal  with  small  appliances;  but  if  his 
work  is  done  in  a  perfunctory  manner,  then  the  best  equipment  in 
the  world  will  serve  him  but  scantily." 

Although  this  book  has  been  prepared  with  a  view  to  laboratory 
work,  it  may,  in  common  with  all  text-books,  be  used  as  a  mere  cram- 
book.  It  may  be  advantageously  used  by  those  teachers  who  prefer 
or  are  compelled,  by  a  real  or  a  supposed  want  of  time,  to  perform 
experiments  themselves  with  elaborate  apparatus.  Such  apparatus,  if 
the  teacher  possesses  it,  is  best  explained  to  the  pupil  viva  voce,  and 
pictures  of  the  apparatus  are  not  needed,  while  the  book  will  serve  an 
additional  and  an  important  purpose  of  showing  how  the  same  results 
may  be  obtained  in  a  more  simple  way.  The  great  central  ideas 
which  are  kept  prominent  throughout  the  book,  and  which  serve  to 
connect  the  different  departments  of  Physics  in  one  coherent  whole, 
are  the  doctrines  of  the  conservation  of  energy  and  the  correlation 
of  forces.  So  far  as  practicable,  experiments  precede  the  statements 
of  definitions  and  laws,  and  the  latter  are  not  given  until  the  pupil 
is  prepared,  by  previous  observation  and  discussion,  to  frame  them  for 
himself.  The  subjects  are  so  arranged  that,  in  case  a  year  is  devoted 
to  this  study,  Heat  and  Electricity  may  be  studied  in  the  winter 
months,  and  Light  in  the  sunny  days  of  summer. 

Many  problems  are  given  in  connection  with  the  various  principles 


VI 

and  laws.  It  is  not  expected  that  all  pupils  will  perform  all  the 
problems ;  but  the  teacher  will  select  judiciously  from  them.  If  the 
minds  of  the  pupils  are  quite  immature,  or  the  time  devoted  to  this 
study  is  very  limited,  it  would  be  advisable  to  omit  some  of  the 
more  difficult  topics ;  such,  for  instance,  as  are  treated  in  §§  93-97, 
and  others.  Most  teachers  prefer  the  "  too  much  "  to  the  "  too  little." 

Every  teacher  has  a  method  of  his  own.  But  perhaps  the  follow- 
ing plan,  practised  by  the  author,  may  be  suggestive  to  some :  He 
divides  the  experiments  into  three  classes:  home,  laboratory,  and 
lecture-room  experiments.  The  first  class  is  indicated  in  the  assign- 
ment of  a  lesson.  They  are  such  as  may  be  performed  with  such 
simple  means  as  every  pupil  has  at  his  home.  The  laboratory  experi- 
ments are  conducted  as  follows :  Suppose  that  the  number  of  pupils 
engaged  at  one  time  is  fifteen,  about  as  many  as  one  teacher  can  care 
for  successfully,  and  that  the  number  of  experiments  to  be  performed 
during  the  hour  is  five,  which  is  about  an  average  number;  then,  tt> 
save  a  multiplicity  of  apparatus  of  the  same  kind,  only  three  sets  of 
apparatus  of  a  kind  are  provided  for  each  experiment.  As  soon  as  a 
pupil  completes  an  experiment  with  one  piece  of  apparatus,  he  looks 
about  for  an  idle  piece  of  some  other  kind;  or,  finding  none, 
he  improves  the  time  in  writing  notes  on  his  experiments  until 
apparatus  is  ready  for  him;  in  this  way  each  pupil  performs  five 
experiments  during  the  hour,  and  devotes  an  average  time  of  twelve 
minutes  to  each  experiment,  including  the  time  of  writing  notes. 
The  third  class  of  experiments  includes  such  as  require  the  use  of 
apparatus  that  cannot  safely  be  placed  in  the  hands  of  pupils, — a 
very  limited  number,  —  and  those  which  have  been  performed  by 
the  pupils,  and  which  the  teacher  may  wish  to  repeat  in  a  more 
elaborate  way. 

Laboratory  practice  and  didactic  study  should  go  hand  in  hand, 
and  divide  time  with  one  another  about  equally.  In  general,  let  the 
experiment  precede  the  instruction,  the  pupils  being  guided  in  their 
investigations  in  the  proper  channels  by  the  book  and  by  blackboard 


AUTHOR'S  PREFACE.  vii 

directions.  Do  not  teach  pupils  to  swim  before  entering  the  water. 
Supt.  Seaver,  in  another  part  of  his  report,  exclaims :  — 

"How  many  of  our  text-books  begin,  not  with  the. suggestion  of 
concrete  illustrations,  but  with  abstract  definitions,  and  still  more 
abstract  'first  principles,' —  blind  guides  to  the  blind  teacher,  and 
sources  of  perplexity  to  teachers  who  are  not  blind,"  etc. 

Why  should  the  pupil  so  frequently,  to  his  great  discouragement, 
be  called  upon  to  break  through  a  wall  of  such  difficulties  before 
coming  in  contact  with  Nature? 

The  author  would  take  this  occasion  to  acknowledge  with  pro- 
found thanks  his  indebtedness  to  many  distinguished  professors  of 
Physics  for  valuable  assistance.  Professor  C.  K.  Wead  of  Michigan 
University  has  read  the  entire  work  in  manuscript,  and  Dr.  C.  S. 
Hastings  of  Johns  Hopkins  University  has  read  the  larger  portion 
in  manuscript  and  the  remainder  in  proof-sheets;  and  their  many 
practical  suggestions  have  largely  contributed  to  whatever  of  success 
may  have  been  achieved.  Prof.  T.  C.  Mendenhall  of  the  Ohio  State 
University  has  rendered  valuable  assistance  in  the  preparation  of  the 
summary  of  mechanical  formulas  and  units  on  page  128,  as  well  as 
in  the  revision  of  the  proofs.  To  Professors  A.  E.  Dolbear,  Tufts 
College ;  C.  R.  Cross  and  S.  W.  Holman,  Mass.  lust,  of  Technology ; 
C.  F.  Emerson,  Dartmouth  College ;  J.  E.  Davies,  University  of  Wis- 
consin; B.  C.  Jillson,  Western  University  of  Pennsylvania;  A.  C. 
Perkins,  Exeter  Academy ;  J.  E.  Vose,  Gushing  Academy,  Ashburn- 
ham;  J.  O.  Norris,  East  Boston  High  School;  G.  C.  Mann,  Jamaica 
Plain  High  School ;  and  others,  who  have  kindly  and  patiently  read 
and  criticised  the  proofs  as  they  have  passed  through  the  press,  our 
hearty  thanks  are  due. 

Under  the  guidance  and  counsel  of  such  an  array  of  distinguished 
instructors,  we  may  well  feel  a  degree  of  confidence  that  the  teachings 
of  the  book  are  not  far  wrong.  Yet  it  should  be  distinctly  under- 
stood, that  for  any  errors  which  may  have  crept  into  the  book,  the 
author  holds  himself  entirely  responsible. 


CONTENTS. 


CHAPTER  I. 
MATTER  AND    ITS    PROPERTIES. 

PAGE 

Introduction.  —  Molecule.  —  Constitution  of  matter.  —  Physical 
and  chemical  changes.  —  Force.  —  Three  states  of  matter.  — 
Phenomena  of  attraction,  —  adhesion,  cohesion,  etc 1 


CHAPTER  II. 
DYNAMICS. 

Dynamics  of  fluids.  —  Pressure  in  fluids.  —  Barometer.  — Compres- 
sibility and  expansibility  of  fluids.  —  Transmitted  pressure.  — 
Siphon.  —  Apparatus  for  raising  liquids.  —  Buoyant  force  of 
fluids.  —  Specific  gravity.  —  Motion.  —  Laws  of  motion.  — 
Composition  and  resolution  of  forces.  —  Center  of  gravity.  — 
Curvilinear  motion.  —  Accelerated  and  retarded  motion.  — 
The  pendulum.  —  Momentum.  —  Work  and  energy.  —  Trans- 
formation of  energy.  —  Machines 44 


CHAPTER  III. 
MOLECULAR  ENERGY.  —  HEAT. 

Heat  defined.  —  Temperature.  —  Diffusion  of  heat.  —  Effects  of 
heat.  —  Expansion.  —  Thermometry.  —  Laws  of  gaseous 
bodies.  —  Laws  of  fusion  and  boiling.  —  Heat  convertible  into 
potential  energy,  and  vice  versa.  —  Specific  heat.  —  Thermo- 
dynamics. —  Steam  engine 138 


X  CONTENTS. 

CHAPTER   IV. 
ELECTRICITY    AND    MAGNETISM. 

PAGE 

Current  electricity.  —  Batteries.  —  Effects  produced  by  electricity. 

—  Electrical    measurements.  —  Magnets    and    magnetism.  — 
Laws  of  currents.  —  Magneto-electric  and  current  induction. 
— Thermo-electricity.  — Frictional  electricity.  —  Electrical  ma- 
chines. —  Applications  of  electricity 179 

CHAPTER  V. 
SOUND. 

Vibration  and  waves.  —  Sound-waves.  —  Velocity  of  sound.  —  Re- 
flection and  refraction  of  sound.  —  Loudness.  —  Interference. 

—  Forced  and  sympathetic  vibrations.  —  Pitch.  —  Vibration  of" 
strings.  —  Overtones   and  harmonics.  —  Quality.  —  Composi- 
tion of  sonorous  vibrations.  —  Sound-receiving  instruments. 

—  Musical  instruments 272 

CHAPTER  VI. 
RADIANT   ENERGY.  —  LIGHT. 

Introduction.  —  Photometry.  —  Reflection.  —  Refraction.  —  Spec- 
trum analysis.  —  Color.  —  Interference.  —  Refraction  and 
polarization.  —  Thermal  effects  of  radiation.  —  Optical  instru- 
ments   325 

APPENDIX  .  399 


ELEMENTS  OF  PHYSICS. 


ELEMENTS  OF  PHYSICS, 

CHAPTER  I. 

MATTER   AND    ITS    PROPERTIES. 

I.   INTRODUCTION. 

§1.  Experimentation.  —  An  experiment  is  a  question  put 
to  Nature.  We  receive  the  answer  by  means  of  a  phenomenon, 
—  that  is,  a  change  which  we  observe,  sometimes  by  the  sight 
or  hearing,  sometimes  by  other  senses.  In  every  experiment, 
certain  facts  or  conditions  are  alwa}*s  known ;  and  the  inquiry 
consists  in  ascertaining  the  facts  or  conditions  that  follow  as  a 
consequence.  The  following  experiments  and  discussions  will 
illustrate :  — 

§  2.  Things  known  and  things  to  be  ascertained. — We 
are  certain  that  we  cannot  make  our  right  hand  occupy  the  same 
space  with  our  left  hand  at  the  same  time.  All  experience 
teaches  us  that  no  two  portions  of  matter  can  occupy  the  same 
space  at  the  same  time.  This  property  which  matter  possesses 
of  excluding  other  matter  from  its  own  space,  is  called  impene- 
trability. It  is  peculiar  to  matter;  nothing  else  possesses  it. 
These  facts  being  known,  let  us  proceed  to  put  certain  inter- 
rogatories to  Nature.  Is  air  matter?  Is  a  vessel  full  of  air 
a  vessel  full  of  nothing  ?  Is  it  "  empty  "  ?  Can  matter  exist  in 
an  invisible  state? 

Experiment  1.  Float  a  cork  on  a  surface  of  water,  cover  it  with  a 
tumbler  or  tall  glass  jar,  and  thrust  the  glass  vessel,  mouth  downward, 


MATTER   AND   ITS   PROPERTIES. 


into'*  the  -water. 


In  case  a  tall  jar  (Fig.  1)  is  used,  the  experiment 
'  '-may  be  made  more  attractive  by  placing  on  the  cork 
•  '*a  lighted  candle.    State  how  the  experiment  answers 
each  of  the  above  questions,  and  what  evidence  it 
furnishes  that  air  is  matter ;  or,  at  least,  that  air  is 
like  matter. 

Experiment  2.  Hold  a  test-tube  for  a  minute 
over  the  mouth  of  a  bottle  containing  ammonia 
water.  Hold  another  tube  over  a  bottle  containing 
hydrochloric  acid.  The  tubes  become  filled  with 
gases  that  rise  from  the  bottles,  yet  nothing  can 
be  seen  in  either  tube.  Place  the  mouth  of  the  first 
tube  over  the  mouth  of  the  second,  and  invert. 
Straightway  a  white  cloud  appears  in  the  tubes. 
Soon  a  white,  flaky  solid  collects  on  the  bottom  of 
the  lower  tube.  Surely,  out  of  nothing  we  cannot 
create  something.  Which  one  of  the  above  ques- 
tions does  this  experiment  answer  ?  How  does  the  experimei'-  an- 
swer it  ? 

Again,  we  are  quite  familiar  with  the  fact  that  matter  exerts  a 
downward  pressure  on  things  upon  which  it  rests ;  and  that 
matter,  in  a  liquid  stste  at  least,  exerts  pressure  in  other  direc- 
tions than  downward,  as,  for  instance,  against  the  sides  of  the 
containing  vessel.  Does  air  exBrt  pressure  ? 

Experiment  3.  Thrust  a  tumbler,  mouth  downward,  into  water, 
and  slowly  invert.  You  see  bubbles  escape  from  the 
mouth.  What  is  this  that  displaces  the  water,  and 
forms  the  bubbles?  When  the  tumbler  becomes  filled 
with  water,  once  more  invert,  keeping  its  nfouth 
under  the  surface  of  the  water,  and  raise  it  nearly  out 
of  the  water,  as  in  Figure  2.  The  water  does  not 
fall  out  of  the  tumbler,  but  remains  in  it,  entirely 
filling  it.  Hence,  there  is  some  pressure  exerted  on 
the  free  surface  of  the  water;  otherwise,  the  level 
would  be  the  same  in  the  two  communicating  vessels. 
This  pressure  on  the  surface  of  the  water  can  only  be 
produced  by  some  body  resting  thereupon.  But  there 

is  no  body,  except  the  air,  that  rests  upon  it.     What  conclusion  do 

7011  draw  from  this? 


Fig.  2. 


MINUTENESS   OF    PARTICLES    OF   MATTER. 


Experiment  4.  Pass  a  glass  tube  through  the  stopper  of  a  bottle 
(Fig.  3).  Attach  a  rubber  tube  to  the  glass  tube.  Exhaust 
the  air  by  "suction"  from  the  bottle;  pinch  the  rubber 
tube  in  the  middle,  insert  the  open  end  into  a  basin  of 
water,  and  then  release  the  tube.  What  causes  the  water 
to  enter  the  bottle  ?  Why  does  not  the  water  fill  the  bot- 
tle ? 

Finally,  we  know  that  matter  has  weight,  and  noth- 
ing else  has  it.  Has  air  weight? 

Experiment  5.  Exhaust  the  air  by  means  of  an  air- 
pump  from  a  hollow  globe  (Fig.  4).  Having  turned  the 
stop-cock  to  prevent  the  entrance  of  air,  carefully  balance 
the  globe  on  a  scale-beam,  as  in  Figure  5.  Afterwards  turn 
the  stop-cock,  and  admit  the  air.  The  globe  is  no  longer 
balanced.  Once  more  apply  weights  till  it  is  balanced. 

The  experiments  with  air  teach  us  that  it  is  matter, 
since,  like  matter,  it  can  exclude  other  matter  from  the  space  it 
occupies,  it  exerts  pressure,  and  has  weight,  while  all  the  above 
experiments  draw  from  nature  one  reply,  MATTER  CAN  EXIST  IN 

AN    INVISIBLE    STATE. 


Fig.  4. 


Fig.  5. 


§  3.  Minuteness  of  particles  of  matter.  —  Physiologists 
teach  us,  that,  in  order  to  smell  any  substance,  we  must  take 

into    our    nostrils,    as   we 

breathe,  small  particles  of 

that   substance  which   are 

floating   in   the   air.     The 

air,     for     several     meters 

around,  is  sometimes  filled 

with  fragrance  from  a  rose. 

You  cannot  see  anything 

in  the  air,  but  it  is,  never- 
theless, filled  with  a  very 

fine  dust  that  floats  away  from  the  rose.  The  odor  of  rosemary 
at  sea  renders  the  shores  of  Spain  distinguishable  long  before 
the}r  are  in  sight.  A  grain  of  musk  will  scent  a  room  for  many 


4  MATTER  AND    ITS   PROPERTIES. 

years,  by  constantly  sending  forth  into  the  air  a  dust  of  musk. 
Though  the  number  of  particles  that  escape  must  be  countless, 
yet  they  are  so  small  that  the  original  grain  does  not  lose 
perceptibly  in  weight. 

The  microscope  enables  us  to  see,  in  a  single  drop  of  stagnant 
water,  a  world  of  living  creatures,  swimming  with  as  much  liberty 
as  whales  in  a  sea.  The  larger  prey  upon  the  smaller,  and  the 
smaller  find  their  food  in  the  still  smaller,  and  so  on,  till  the 
power  of  the  microscope  fails  us.  The  whale  and  the  minnow 
do  not  differ  more  in  size  than  do  some  of  these  animalcules,  the 
largest  of  which  are  hardly  visible  to  the  naked  eye.  But  as 
the  smallest  of  these  perform  very  complex  operations  in  col- 
lecting and  assimilating  food,  we  must  conclude  that  the}7  are 
composed  not  only  of  many  particles,  but  of  many  kinds  of 
matter.  These  minute  living  forms  that  people  the  microscopic 
world  are  exceedingly  large,  in  comparison  with  the  incon- 
ceivably minute  particles  called  molecules,  which  physicists  now 
"  measure  without  seeing." 

§  4.  The  molecule.  —  Experiment  1.  Examine  carefully  a  drop 
of  water  with  the  naked  eye,  or  with  a  microscope.  So  far  as  you  are 
able  to  see,  the  space  occupied  by  the  drop  is  entirely 
filled  with  water.  Fill  a  test-tube  with  water  (Fig.  6). 
Insert  a  cork  stopper,  pierced  with  a  glass  tube ;  heat 
over  a  lamp-flame,  and  note  the  phenomena  produced. 
The  water  expands,  and  rises  in  the  smaller  tube;  still 
the  test-tube  seems  to  be  full  of 

Fig   7 

water.    Place  it  in  ice-water,  and 
the  water  contracts. 

Expand- 

This  change  of  volume  can    ' 
be  explained  only  on  one  of 
two    suppositions  :    the    space   contract- 
occupied  by  the  water  may,  as 
it   appears,  be   full   of  water, 
which  the  heat  causes  to  expand,  and  occupy  a  greater  space,  as 
represented  graphically  in  Figure  7  ;  or  the  body  of  water  may 


THE  MOLECULE.  5 

consist  of  a  definite  number  of  distinct  particles  called  molecules 
(as  represented  in  Figure  8),  separated  from  one  another  by 
spaces  so  small  as  not  to  be  perceptible, 
even  with  the  aid  of  a  microscope.  Expan- 
sion,  in  this  case,  is  accounted  for  by  a  simple 
separation  of  molecules  to  greater  distances. 
There  is  no  increase  in  the  number  of  mole- 
cules, no  increase  in  their  size,  only  an  en- 
largement of  space  between  them.  Which 
of  these  suppositions  is  the  more  probable  ? 

Experiment  2.    Place  a  tumbler  full  of  cold 
water  in  a  warm  place,  and  in  about  an  hour 

examine  it.  You  find  many  small  bubbles  of  air  clinging  to  all  parts 
of  the  interior  surface  of  the  glass.  Is  it  probable  that  outside  air 
has  descended  into  the  liquid? 

Experiment  3.  Place  a  tumbler  half  full  of  water  under  a  glass 
receiver  of  an  air-pump  (page  54),  and  exhaust  the  air.  When  a  very 
good  vacuum  has  been  obtained,  bubbles  of  air  will  be  seen  to  form 
at  all  points  in  the  liquid,  and  to  rise  and  burst  near  the  surface. 

Evidently  the  air  was  previously  in  the  same  space  occupied 
by  the  water.  This  seems  to  contradict  the  first  of  the  above 
suppositions  ;  for,  according  to  that,  the  space  occupied  by  the 
water  is  full  of  water,  leaving  no  room  for  other  matter.  But 
according  to  the  second  supposition,  the  space  is  not  filled  with 
water ;  there  is  still  room  for  particles  of  other  matter  in  the 
spaces  among  the  molecules  of  water.  Now,  as  we  cannot  con- 
ceive of  two  portions  of  matter  occupying  the  same  space  at 
the  same  time  (e.g.,  where  air  is,  water  cannot  be),  we  con- 
clude that  the  glass  ' '  full  of  water ' '  is  not  full  of  water.  In  a 
similar  manner,  it  may  be  shown  that  no  visible  body  com- 
pletely fills  the  space  enclosed  by  its  surface,  but  that  there  are 
spaces  in  every  body  that  may  receive  foreign  matter.  If  there 
are  spaces,  then  the  bodies  of  matter  that  our  eyes  are  per- 
mitted to  see  are  not  continuous^  as  space  is  continuous.  But 
every  visible  body  is  an  aggregation  of  a  countless  number  of 
separate  and  individual  bodies  called  molecules. 


6  MATTER   AND   ITS   PROPERTIES. 

Perform,  at  your  homes,  the  two  following  experiments : 

Experiment  4.  Pulverize  one-half  of  a  teaspoonful  of  starch,  and 
boil  it  in  two  tablespoonfuls  of  water,  stirring  it  meantime.  What 
phenomena  occur?  What  do  they  teach?  What  becomes  of  the 
water  ? 

Experiment  5.  Fill  a  bowl  half  full  with  peas  or  beans.  Just  cover 
them  with  tepid  water,  and  set  away  for  the  night.  Examine  in  the 
morning.  What  phenomena  do  you  observe  ?  Explain  each. 

Strictly  speaking,  are  bodies  of  matter  impenetrable  ?  What 
only  is  impenetrable?  When  you  drive  a  nail  into  wood,  do  you 
make  the  two  bodies  occupy  the  same  space  at  the  same  time  ? 
Do  the  wood  and  the  iron  occupy  the  same  space  ?  How  only 
can  you  explain  this  phenomenon,  consistently  with  the  princi- 
ples of  impenetrability  of  matter  ? 

§  5.  Theory  of  the  constitution  of  matter.  —  For  reasons 
which  appear  above,  together  with  many  others  that  will  appear 
as  our  knowledge  of  matter  is  extended,  physicists  have  gener- 
ally adopted  the  following  theory  of  the  constitution  of  matter. 
Every  visible  body  of  matter  is  composed  of  exceedingly  small 
particles,  called  molecules ;  in  other  words,  every  body  is  the  sum 
of  its  molecules.  No  two  molecules  of  matter  in  the  universe  are 
in  contact  with  each  other.  Every  molecule  of  a  body  is  separated 
from  its  neighbors,  on  all  sides,  by  inconceivably  small  spaces. 
Every  molecule  is  in  quivering  motion  in  its  little  space,  moving 
back  and  forth  between  its  neighbors,  and  rebounding  from  them. 
Wlien  we  heat  a  body  we  simply  cause  the  molecules  to  move  more 
rapidly  through  their  spaces;  so  they  strike  harder  bloivs  on  their 
neighbors,  and  usually  push  them  away  a  very  little;  hence,  the 
size  of  the  body  increases. 

This  theory  seems,  at  first,  little  more  than  an  extravagant 
guess.  But  if  it  shall  be  found  that  this  theory,  and  this  theory 
alone,  will  enable  us  to  account  for  most  of  the  known  phenom- 
ena of  matter,  then  we  shall  be  content  to  adopt  it  till  a  better 
can  be  produced. 


POROSITY.  —  DENSITY.  7 

§  6.  Porosity.  —  If  the  molecules  of  a  body  are  nowhere  in 
absolute  contact,  it  follows  that  there  are  unoccupied  spaces 
among  them  which  may  be  occupied  by  molecules  of  other  sub- 
stances. These  spaces  are  called  pores.  Water  disappears  in 
cloth  and  beans.  It  is  said  to  penetrate  them ;  but  it  really 
enters  the  vacant  spaces  or  pores  between  the  molecules  of  these 
substances.  All  matter  is  porous ;  thus  water  may  be  forced 
through  solid  cast-iron,  and  dense  gold  will  absorb  the  liquid 
mercury  much  as  chalk  will  water.  The  term  pore,  in  physics, 
is  restricted  to  the  invisible  spaces  that  separate  molecules.  The 
cavities  that  may  be  seen  in  a  sponge  are  not  pores,  but  holes  ; 
the}r  are  no  more  entitled  to  be  called  pores,  than  the  cells  of  a 
honeycomb,  or  the  rooms  of  a  house,  are  entitled  to  be  called, 
respectively,  the  pores  of  the  honeycomb  or  of  the  house. 

Small  as  animalcules  are,  they  are  coarse  lumps  in  comparison  with 
the  size  of  the  molecule.  By  means  of  delicate  calculations,  the  physi- 
cist has  succeeded  in  ascertaining  approximately  the  probable  size  of 
the  molecule.  If  a  drop  of  water  could  be  magnified  to  the  size  of  the 
earth,  it  is  thought  that  its  molecules  would  appear  smaller  than  an 
apple.  In  other  words,  the  molecule,  in  size,  is  to  a  drop  of  water 
what  an  apple  is  to  the  earth.  If  we  should  attempt  to  count  the  num- 
ber of  molecules  in  a  pin's  head,  counting  at  the  rate  of  ten  million  in 
a  second,  we  should  require  250,000  years. 

§  7.  Density.  —  Cut  several  blocks  of  wood,  apple,  putty, 
lead,  etc.,  of  just  the  same  size,  and  weigh  them.  Do  they  have 
the  same  weight?  Can  you  explain  the  difference  by  a  differ- 
ence of  porosity? 

Again,  if  you  can  try  the  experiment  illustrated  in  Figs.  4  and 
5,  using  various  gases,  you  will  find  that  the  weights  of  the  same 
volumes  of  different  gases  are  different.-  But  the  chemist  has 
reasons  for  believing  that  there  is  the  same  number  of  molecules 
in  the  globe  whatever  be  the  gas,  if  the  pressure  and  the  tem- 
perature are  the  same.  We  see  then  that  some  bodies  have  more 
matter  in  a  given  volume  than  others,  either  because  the  molecules 
are  closer  together,  or  because  the  molecules  are  different ;  we  call 


8  MATTER   AND    ITS   PROPERTIES. 

them  more  dense.  By  the  mass  oj  a  body  we  understand  the 
quantity  of  matter  in  it;  and  by  its  density,  the  mass  in  the  unit 
volume  of  it.  For  example,  the  density  of  cast-iron  is  about 
450  pounds  per  cubic  foot. 

§  8.  Simple  and  compound  substances.  —  Place  a  small 
quantity  of  sugar  on  a  hot  stove.  In  a  few  minutes  it  changes 
to  a  black  mass.  This  black  substance  is  found  to  be  char- 
coal, or  carbon,  as  chemists  call  it.  Evidently  the  sugar  must 
have  contained  carbon,  for  the  carbon  came  from  the  sugar. 
Chemists  are  also  able  to  obtain  water  from  sugar.  The  heat, 
in  our  experiment,  expels  the  water  in  the  form  of  steam,  and 
leaves  the  carbon.  Carbon  can  be  extracted  from  sugar  in 
another  way.  Prepare  a  very  thick  s}Tup,  by  dissolving  sugar 
in  hot  water,  and  pour  upon  the  syrup  two  or  three  times  its 
bulk  of  sulphuric  acid.  You  will  quickly  obtain  a  bulky,  spongy 
mass  of  carbon. 

By  suitable  processes,  there  may  be  obtained  from  marble 
three  substances,  each  one  of  which  is  entirely  unlike  marble. 
One  of  the  substances  is  carbon ;  another  is  a  metal  called  cal- 
cium, which  looks  very  much  like  silver  ;  the  third  is  a  gas  called 
ox3Tgen,  which,  when  set  free  from  its  prison-house  in  the  solid, 
expands  to  many  times  the  size  of  the  marble  from  which  it  was 
liberated. 

If  we  should  grind  a  small  piece  of  marble  for  many  hours  in 
a  mortar,  we  should  reduce  the  marble  to  a  very  fine  powder, 
but  should  fall  very  far  short  of  reducing  it  to  its  molecules. 
Still,  each  little  particle  of  the  powder  is  as  truly  marble  as  the 
original  lump.  If  we  should  continue  the  division,  in  our  imagi- 
nations, till  the  marble  were  reduced  to  molecules,  we  should 
expect  to  find  all  the  molecules  just  alike.  Now,  since  our 
smallest  piece,  our  molecule,  our  unit  of  marble,  is  marble,  and 
since  marble  is  composed  of  the  three  substances,  carbon,  cal- 
cium, and  oxygen,  we  conclude  that  our  molecule  itself  must  be 
capable  of  division.  No  one  has  been  able  to  separate  any  one 


PHYSICAL   AND   CHEMICAL   CHANGES.  9 

of  these  substances  into  other  substances.  No  one  has  taken 
away  from  calcium  anything  but  calcium,  or  extracted  from 
carbon,  or  from  oxygen,  anything  but  carbon  and  oxygen. 

Those  substances  that  have  resisted  all  efforts  to  break  them 
up  into  other  substances  are  called  simple  substances  or  ele- 
ments. Those  substances  that  may  be  broken  up  into  other 
substances  are  called  compound  substances.  Of  the  large  num- 
ber of  substances  known  to  man,  only  71  are  elements.  All 
other  substances  are  compounds  of  two  or  more  of  these  71 
elements. 

A  molecule  of  any  substance,  simple  or  compound,  is  that 
minute  mass  of  the  substance  which  cannot  be  divided  without 
destroying  its  properties. 

§  9.  Physical  and  chemical  changes.  —  When  sugar  is 
ground  to  a  powder,  the  particles  are  simply  torn  apart,  but  do 
not  lose  their  characteristics.  The  powder  is  just  as  sweet  as  the 
lump.  Such  a  division  is  called  &  physical  division.  Generally, 
any  change  in  a  substance  that  does  not  cause  it  to  lose  its  identity, 
in  other  words,  to  cease  to  be  that  substance,  is  called  a  physical 
change.  When  sufficient  heat  is  applied  to  sugar,  the  molecules 
themselves  are  divided  ;  and  when  a  molecule  of  sugar  is  divided, 
the  result  is  not  two  parts  of  a  molecule  of  sugar,  but  the  two 
substances,  carbon  and  water.  The  sweetness  is  destroyed  • 
sugar  no  longer  exists ;  other  substances  have  taken  its  place. 
The  molecule  of  sugar  is  no  more  like  the  substances  into  which 
it  has  been  separated,  than  a  word  is  like  the  letters  that  com- 
pose it.  Such  a  division  is  called  a  chemical  division.  Gener- 
ally, any  change  in  a  substance  that  causes  it  to  lose  its  identity, 
or  cease  to  be  that  substance,  is  called  a  chemical  change. 

Ice,  heated,  melts  to  water;  water,  heated,  becomes  steam;  steam, 
cooled,  condenses  to  water;  water,  cooled,  becomes  solid.  During 
these  changes  the  substance,  the  molecule,  has  not  changed.  There 
has  been  only  a  change  among  the  molecules,  in  distance  and  arrange- 
ment. What  kind  of  change  is  this?  But  if  the  steam  is  subjected  to 
a  very  intense  heat,  the  result  is  that  it  becomes  converted  into  a 


10  MATTER   AND  ITS  PROPERTIES. 

mixed  gas,  consisting  of  two  gases,  oxygen  and  hydrogen.  This  gas 
is  not  condensable  at  any  ordinary  temperature.  Unlike  steam,  it 
burns  and  even  explodes.  What  kind  of  separation  is  this  ?  What 
has  been  separated  ? 

Blackboard  crayons  are  prepared  by  subjecting  the  dust  of  plaster 
of  Paris  to  great  pressure,  which  causes  the  particles  to  unite  and  form 
the  crayon.  What  kind  of  change  is  this?  What  kind  of  union?  In  the 
experiment  (page  2)  with  the  ammonia  and  hydrochloric-acid  gases, 
the  two  gases  disappear,  and  a  solid  is  left  in  their  place.  What  kind 
of  change  is  this :  chemical  or  physical?  Is  it  union  or  separation? 

§  10.  Annihilation  and  creation  of  matter  impossible. 
—  Experiment  1.  Prepare  a  saturated  solution  of  calcium  chloride. 
Mix  with  an  equal  bulk  of  water  and  weigh  the  solution.  Prepare  a 
dilute  solution  of  sulphuric  acid  (1  to  4),  and  pour  an  equal  weight  of 
the  last  solution  on  the  first,  all  at  once,  and  shake  gently.  Instantly 
the  mixed  liquid  becomes  a  solid.  The  solid  formed  is  commonly 
called  plaster  of  Paris.  It  is  an  entirely  different  substance  from 
either  of  the  two  liquids  used.  What  kind  of  change  is  this  ?  A  new 
substance  has  been  formed.  Has  matter  been  created?  Weigh  the 
resulting  solid ;  its  weight  equals  the  sum  of  the  weights  of  the  two 
liquids.  The  conclusion  is,  that  no  matter  has  been  created,  none 
lost. 

Solids  may  be  converted  into  liquids  or  gases  ;  gases  may  be 
converted  into  liquids  or  solids  ;  substances  may  completely  lose 
their  characteristics :  but  man  has  not  discovered  the  means  by 
which  a  single  molecule  of  matter  can  be  created  out  of  nothing, 
or  by  which  a  single  molecule  of  matter  can  be  reduced  to 
nothing.  Matter  cannot  be  created,  cannot  be  annihilated ;  it 
is  a  constant  quantity.  The  discovery  of  this  fact  laid  the 
foundation  of  the  science  of  Chemistry. 

This  statement  may  not  seem  to  accord  with  many  occurrences  of 
every-day  experience.  Wood,  coal,  and  other  substances  burn ;  matter 
disappears,  and  very  little  is  left  that  can  be  seen.  But  does  matter 
pass  out  of  existence  when  it  disappears  in  burning,  or  does  it  assume 
the  invisible  state  known  by  the  name  of  gas  ? 

Experiment  2.  Hold  a  cold,  dry  tumbler  over  a  candle-flame.  The 
bright  glass  instantly  becomes  dimmed;  and,  on  close  examination,  you 
find  the  glass  bedewed  with  fine  drops  of  a  liquid.  This  liquid  is  water. 


ANNIHILATION   AND   CREATION   OF   MATTER.  11 

You  may  think  it  strange  that  water  is  formed  in  the  hot  flame; 
yet  this  simple  experiment  shows  that  this  is  really  the  case.  If  water 
is  formed  during  the  burning,  what  is  the  reason  we  do  not  see  it  ? 
Simply  because  it  rises  in  the  form  of  steam,  which  is  an  invisible  gas. 
The  visible  cloud,  often  called  steam,  which  is  formed  in  front  of  the 
nozzle  of  a  tea-kettle,  is  not  steam,  but  fine  drops  of  water  floating  in 
the  air,  —  a  sort  of  water-dust.  All  clouds  are  of  the  same  nature.  A 
cloud  always  stands  over  Niagara  Falls,  even  on  the  clearest  days. 
The  water  of  the  river  falls  a  distance  of  150  feet,  and,  striking  a  bed 
of  rocks  below,  some  of  it  is  dashed  into  fragments,  or  dust,  which 
rises  in  a  cloud. 

Experiment  3.  Introduce  a  candle-flame  into  a  clean  glass  bottle ; 
after  it  has  burned  a  few  minutes  the  flame  goes  out.  Why  does  it 
go  out  ?  See  whether  the  air  in  the  bottle  is  the  same  as  it  was  be- 
fore. Pour  a  wineglass  full  of  lime-water  into  the  bottle,  cover  tight- 
ly, and  shake.  Also  pour  lime-water  into  a  bottle  filled  with  air.  The 
former  becomes  white  and  cloudy,  the  latter  remains  clear.  It  is 
apparent  that  some  new  substance  has  been  formed  during  the 
burning,  which,  unlike  air,  can  turn  the  lime-water  white.  This  new 
substance  is  likewise  an  invisible  gas. 

So  that,  before  we  can  decide  whether  or  not  matter  is  annihilated 
while  burning,  it  is  necessary  to  collect  carefully,  not  only  the  ashes, 
but  all  the  invisible  gases  that  are  formed.  This  is  a  somewhat 
troublesome  experiment ;  but  it  has  been  frequently  performed,  and  it 
is  found  that  their  collective  weight  is  quite  equal  to  the  weight  which 
the  candle  loses. 

Water  does  not  pass  out  of  existence  when  it  "  dries  up  " ;  nor  are 
raindrops  and  dewclrops  created  out  of  nothing.  Matter  is  everywhere 
undergoing  great  and  various  changes,  both  chemical  and  physical. 
Nature  is  ever  arraying  herself  in  new  forms.  The  sun  warms  the 
tropical  ocean,  converting  the  liquid  into  vapor;  the  vapor  rises  in 
tlie  air,  is  recondensed  on  mountain  hights,  and  returns  in  rivers  to 
the  ocean  whence  it  came.  Geology  teaches  us  that  continents  and 
oceans,  and  even  the  "everlasting  hills,"  have  a  birth  and  decay,  as 
well  as  whole  tribes  of  animals  and  vegetables.  Although  we  may 
be  counted  among  the  living  ten  years  hence,  our  bodies  will,  ere 
that,  have  crumbled  into  dust ;  and  the  matter  that  will  then  compose 
our  bodies  is  to-day  to  be  found  mainly  in  the  earth  upon  which  we 
tread.  Change  is  stamped  upon  all  matter ;  nothing  is  exempt.  Only 
the  quantity  of  matter  remains  unchanged. 


12  MATTER   AND   ITS   PROPERTIES. 

§  11.  Force.  —  Experiment  1.  From  a  piece  of  cardboard  sus- 
pend, by  means  of  silk  threads,  six  pith-balls,  so  that  they  may  be 

about  2cml  apart.  Procure  a 
clean,  dry  glass  tube,  about 
40cm  long  and  3cm  in  diam- 
eter. Rub  a  portion  of  this 
tube  briskly  with  a  silk  hand- 
kerchief, and  hold  it  about 
2cm  below  the  balls.  The  balls 
seem  to  become  suddenly  pos- 
sessed of  life.  They  gather 
about  the  rod,  and  strive  to 
reach  it.  If  we  cut  one  of 
the  threads,  the  ball  will  fly 

straight  to  the  rod,  and  cling  to  it  for  a  time.  The  means  by  which 
the  rod  pulls  the  balls  is  invisible.  Yet  evidence  is  positive  that  the 
rod  has  an  influence  on  the  balls,  —  that  it  pulls  them.  Slip  a  piece  of 
glass  between  the  rod  and  the  balls ;  still  the  influence  is  felt  by  the 
balls.  The  glass  does  not  sever  the  invisible  bonds  that  connect  the 
balls  with  the  rod. 

Now  slowly  bring  the  rod  near  the  balls,  till  they  touch.  They  at 
first  cling  to  the  rod;  but  soon  the  rod,  as  if  displeased  with  their 
company,  begins  to  push  them  away.  Withdraw  the  rod;  the  balls 
do  not  hang  by  parallel  threads  as  before,  but  appear  to  be  pushing 
one  another  apart.  Gradually  bring  the  palm  of  the  hand  up  beneath 
the  balls,  but  without  touching  them.  The  balls  gradually  yield  to 
the  pull  of  the  hand,  and  come  together.  Remove  the  hand,  and 
they  again  fly  apart.  Matter  does  not  seem  to  be  the  dead,  inert 
thing  which  it  is  often  called ;  it  can  push  and  pull. 

Experiment  2.  Raise  one  of  these  balls  with  the  fingers,  and  then 
withdraw  the  fingers.  Something  from  below  seems  to  reach  up,  and 
pull  the  ball  down  again.  The  same  happens  with  each  one  of  the 
balls ;  every  ball  is  pulled  by  something  below.  What  is  it  that  pulls 
the  balls?  Carry  the  balls  into  another  room,  the  same  thing  occurs. 
Carry  them  to  any  part  of  the  earth,  the  same  thing  occurs.  It  must 
be  that  it  is  the  earth  itself  that  pulls  the  balls.  The  earth  pulls  the 
fruit  and  the  leaf  from  the  tree  to  itself ;  it  pulls  all  objects  to  itself ; 
and  more,  —  it  holds  them  there.  Attempt  to  raise  anything  from  the 
ground,  and  you  feel  the  earth's  pull  resisting  you. 

Attempt  to  break  a  string,  or  crush  a  piece  of  chalk,  and  you  find 

1  Tables  of  the  Metric  Measures  may  be  found  in  the  Appendix,  Section  A. 


MOLAR   AND   MOLECULAR   FORCES.  13 

that,  notwithstanding  the  molecules  of  these  bodies  do  not  touch  one 
another,  they  possess  a  force  which  tends  to  keep  them  together,  and 
to  resist  your  attempt  to  separate  them. 

§  12.  Force  defined.  —  This  tendency  to  push  and  to 
pull,  which  matter  possesses,  is  called  force.  We  do  not 
know  why  separate  portions  of  matter  tend  to  approach  one 
another,  or  to  separate  from  one  another.  We  do  not  know  the 
nature  of  force ;  we  cannot  see  it  or  grasp  it ;  we  simply 
know  that  there  must  be  a  cause  for  certain  effects  produced. 
The  familiar  effects  produced  are  motion  and  rest.  For  exam- 
ple, we  see  a  body  move  ;  we  know  that  there  is  a  cause :  that 
cause  we  attribute  to  force.  When  a  body  in  motion  comes  to 
rest,  we  look  for  a  cause,  and  that  cause  we  attribute  to  force. 
It  is  difficult  to  define  force ;  probably  the  most  comprehensive 
definition  that  has  been  given  is  the  following :  Force  is  that 
which  can  produce,  change,  or  destroy  motion. 

All  force  exhibits  itself  in  pushes  or  pulls.  All  motion  is 
produced  by  pushes  or  pulls,  or  by  a  combination  of  both.  A 
pulling  force  is  called  an  attractive  force,  or  simply  attraction. 
A  pushing  force  is  called  a  repellent  force,  or  repulsion. 

§  13.  Attraction  and  repulsion  mutual.  —  Experiment. 

Suspend  a  wooden  lath  in  a  sling.  Rub  one  end  of  a  glass  rod  with 
silk,  and  bring  that  end  of  the  rod  near  to  one  end  of  the  lath.  The 
lath  is  attracted  by  the  rod  and  moves  toward  it.  Now  place  the  rod 
in  the  sling,  and  bring  the  lath  near  to  its  excited  end.  The  lath  draws 
the  rod  to  itself.  We  conclude  that  the  pulling  force  belongs  to  both 
—  that  both  are  concerned  in  the  pulling.  In  the  experiment  with  the 
pith-balls  (§11,  Exp.  1),  they  seem  to  be  mutually  pushing  each  other. 
All  attraction  and  repulsion  between  different  portions  of  matter  are  mutual. 

§14.  Molar  and  molecular  forces. — The  glass  rod  does 
not  seem  to  possess  any  attractive  force,  until  it  is  rubbed  with 
the  handkerchief.  The  pith-balls  do  not  repel  one  another  until 
they  have  first  touched  the  glass  rod.  After  a  time,  the  rod 
and  the  balls  lose  both  their  attractive  and  repellent  forces. 
Or,  if  we  pass  the  hand  several  times  over  the  part  of  the  rod 


14  MATTER    AND   ITS   PROPERTIES. 

that  has  been  rubbed,  and  over  the  balls,  they  quickly  surrender 
their  forces.  These  forces  are  temporary.  They  are  called 
electric  forces,  and  their  cause  electricity.  The  attractive  force 
that  draws  the  balls  to  the  earth  existed  before  the  experiment. 
No  manipulation  can  destroy  it  or  increase  it ;  it  is  eternal  and 
unchangeable,  and  exists  between  all  portions  of  matter.  This 
force  is  called  the  force  of  gravity,  and  the  phenomenon  is  called 
gravitation. 

We  have  seen  the  effects  of  attractive  and  repellent  forces, 
reaching  across  sensible  distances.  Have  we  any  evidence 
that  these  forces  exist  among  portions  of  matter,  at  insensible 
distances,  i.e.,  at  distances  too  short  to  be  perceived  by  our 
senses  ?  Stretch  a  piece  of  rubber ;  you  realize  that  there  is  a 
force  resisting  you.  You  reason  that  if  the  supposition  be  true, 
that  the  grains  or  molecules  that  compose  the  piece  of  rubber  do 
not  touch  each  other,  then  there  must  be  a  powerful  attractive 
force  reaching  across  the  spaces  between  the  molecules,  to 
prevent  their  separation.  After  stretching  the  rubber,  let  go 
one  end.  It  springs  back  to  its  original  form.  What  is  the 
cause?  Compress  the  rubbe^- ;  its  volume  is  diminished.  (Does 
this  confirm  our  supposition  respecting  the  granular  structure 
of  matter?)  Remove  the  pressure  ;  the  rubber  springs  back  to 
its  original  form.  What  is  the  cause? 

Every  body  of  matter,  with  the  possible  exception  of  the 
molecule,  whether  solid,  liquid,  or  gaseous,  may  be  forced  into 
a  smaller  volume  by  pressure,  —  in  other  words,  matter  is  com- 
pressible. When  pressure  is  removed,  the  body  expands  into 
nearly  or  quite  its  original  volume.  This  shows  two  things : 
first,  that  the  matter  of  which  a  body  is  formed  does  not  really 
Jill  all  the  space  which  the  body  appears  to  occupy;  and,  second, 
that  in  the  body  is  a  force,  which,  acting  from  within  outward, 
resists  outward  pressure  tending  to  compress  it,  and  expands  the 
body  to  its  original  volume  when  pressure  is  removed.  This  is, 
of  course,  a  repellent  force,  and  is  exerted  among  molecules, 
tending  to  push  them  farther  apart. 


MATTEK.  15 

But  it  has  previously  been  shown  that  there  is  also  an  attract- 
ive force  existing  between  the  molecules.  Now  what  is  the 
effect,  when  two  forces  act  on  a  body  in  opposite  directions? 
Let  two  boys,  at  opposite  ends  of  a  table,  push  the  table.  If 
both  push  with  equal  force,  the  table  does  not  move  ;  it  is  as  if 
no  one  pushed  it.  But  if  one  boy  pushes  a  little  harder  than 
the  other,  then  the  table  moves  in  the  direction  in  which  the 
greater  force  is  applied.  Now  we  have  the  key,  to  the  solution 
of  a  difficulty,  which  always  arises  in  the  mind  of  a  beginner  in 
science,  when  he  first  hears  the  startling  statement  that  the 
molecules  of  bodies,  of  his  own  body  even,  do  not  touch  one 
another.  If  faith  were  of  quick  growth,  he  would  shudder  at 
the  thought  of  falling  to  pieces,  or  of  being  wafted  away  by 
the  winds  as  so  much  dust. 

The  ancients,  perceiving  that  matter  must  be  built  up  of 
small  parts,  overcame  this  difficulty  by  supposing  that  the 
minute  particles  have  hooks  or  claws  by  which  they  grasp  one 
another.  Our  knowledge  of  the  operation  of  forces  enables  us  to 
dispense  with  hooks  and  claws,  much  to  the  advantage  of  science. 
We  see  that  the  molecules  of  a  body  are  kept  from  falling 
apart,  or  from  separation,  by  a  universal  attractive  force  ;  they 
are  also  kept  from  falling  together,  or  from  permanent  contact, 
by  an  ever-existing  repellent  force.  These  forces  act  at  insen- 
sible distances  between  molecules,  and  hence  are  called  molecular 
forces.  When  forces  act  between  bodies  at  sensible  distances 
they  are  called  molar  forces.  Give  illustrations  (1)  of  molar 
forces  ;  (2)  of  molecular  forces. 

II.     THREE   STATES   OF  MATTER. 

§  15.  Matter  presents  itself  in  three  different  states :  solid, 
liquid,  and  gaseous,  —  fairly  represented  by  earth,  water,  and 
air.  Because  these  forms  are  so  common  and  abundant,  some 
ancient  philosophers  held  that  all  solid  matter  is  formed  of 
earth,  all  liquids  of  water,  and  all  gases  of  air.  On  this  account 


16  MATTER   AND   ITS   PEOPEETIES. 

they  called  them,  together  with  fire,  elements  or  primary  matter. 
They  cannot  now  be  so  regarded  from  a  chemical  point  of  view, 
because  each  of  them  has  been  separated  into  still  more  simple 
substances ;  nor  from  a  physical  standpoint,  because,  as  will 
soon  be  shown,  most  substances  may  exist  in  any  one  of  these 
states. 

§  16.  Characteristics  of  each  of  these  states. 

Experiment  1.  Provide  two  vessels,  a  cubical  dish  and  a  goblet, 
each  having  a  capacity  of  about  200ccm.  Also  provide  200ccm  of  sand, 
200ccm  of  water,  and  a  cubical  block  of  wood  containing  200ccm. 
Grasp  the  block,  and  place  it  in  the  cubical  vessel.  Attempt  to  do  the 
same  thing  with  the  water.  Why  can  you  not  grasp  the  water  ?  Pour 
a  portion  of  the  water  into  the  cubical  vessel.  When  you  move  a  por- 
tion of  the  block,  the  whole  block  moves.  When  you  pour  a  portion 
of  the  water  into  the  cubical  vessel,  the  whole  does  not  necessarily  go. 
Why  is  this  ?  Why  is  it  that  we  can  dip  a  cupful  of  water  out  of  a 
pailful,  without  raising  the  whole?  Pour  all  the  water  into  the  goblet. 
The  water  adapts  itself  to  the  shape  of  the  goblet,  and  the  vessel  is 
filled.  Attempt  to  place  the  block  of  wood  in  the  goblet.  What  dif- 
ference in  phenomena  do  you  observe  ?  Why  this  difference  ?  Pour 
the  sand  from  vessel  to  vessel.  It  adapts  itself  to  the  shape  of  each 
vessel.  Why  ?  Drop  the  block  of  wood  on  a  table.  Pour  water  on  the 
table.  How  does  a  liquid  behave  when  there  is  no  vessel  to  confine  it  ? 

Experiment  2.  Throw  small  particles  of  sawdust  into  the  goblet  of 
water ;  you  can  thus  render  perceptible  any  motion  of  the  water  in  the 
goblet,  just  as,  by  throwing  blocks  of  wood  on  the  smooth  surface  of 
a  river,  you  can  discover  the  motion  of  the  river.  Notice  the  ease 
with  which  the  particles  move  about,  rise,  and  sink.  As  they  become 
quiet,  slightly  jar  the  vessel,  or  tap  it  with  the  end  of  a  pencil,  and 
notice  the  ease  with  which  disturbance  is  produced  throughout  the 
liquid.  Now  rap  the  side  of  the  block  with  a  hammer,  and  observe 
how  immovable  are  the  particles  of  wood. 

Our  experiments  teach  us  that  the  molecules  of  solids  are  not 
easily  moved  out  of  their  places;  consequently,  solid  masses 
form  such  a  firmly  connected  whole  that  their  shape  is  not  easily 
changed,  and  a  movement  of  one  part  causes  a  movement  of  the 
ii'hole.  On  the  other  hand,  the  molecules  of  liquids  have  scarcely 
any  fixedness  of  position,  but  easily  slip  between  and  around  one 


THREE   STATES   OF   MATTER.  17 

another;  consequent^,  liquid  bodies  easily  mold  themselves  to 
the  shape  of  the  vessel  that  contains  them,  are  poured  from  ves- 
sel to  vessel,  and  are  easily  separated  into  parts. 

But  what  shall  we  say  of  the  sand,  which,  like  water,  adapts 
itself  to  the  shape  of  the  containing  vessel,  and  can  be  poured? 
Is  sand  a  liquid?  and  are  powders  liquids?  No,  powders  are  a 
collection  of  small  lumps  of  solid  matter.  When  powders  are 
poured,  lumps  of  matter  roll  around  one  another,  as  when 
potatoes  are  poured  from  basket  to  basket.  When  liquids  are 
poured,  molecules  glide  past  one  another. 

It  is  not  so  easy  to  study  the  characteristics  of  gases,  because 
we  cannot  usually  see  them.  But  we  may  be  aided  by  a  device 
similar  to  that  employed  to  make  the  movement  of  water  visible. 

Experiment  3.  Darken  a  room,  and  admit,  through  a  small  crack 
or  hole,  a  beam  of  direct  sunlight.  You  see  particles  of  dust  dancing 
in  the  path  of  the  light ;  the  motion  never  ceases.  See  how  easily  the 
motion  is  quickened  by  gently  waving  the  hand  at  some  distance  from 
the  beam  of  light. 

Experiment  4.  Place  under  the  receiver  of  an  air-pump  a  partially 
inflated  balloon,  Fig.  32,  page  53  (or  a  Seven-in-one  apparatus  with  the 
piston  near  the  closed  end  of  the  cylinder,  and  stop-cock  closed),  and 
exhaust  the  air.  The  tendency  of  gases  to  expand  becomes  evident. 

In  gases,  fixedness  of  position  of  the  molecules  is  entirely  want- 
ing, and  freedom  of  motion  among  themselves  is  almost  perfect. 
They  appear  to  be  in  a  continual  state  of  repulsion,  and  conse- 
quently have  a  tendency  to  expand  to  greater  and  greater  volumes. 
They  expand  indefinite^,  unless  confined  by  pressure,  while 
liquids  and  solids  tend  to  preserve  a  uniformity  of  volume. 

Liquids  do  not  rise  above  what  is  called  their  surface,  and  we 
may  have  a  vessel  half  full  of  a  liquid ;  but  gases  have  no  defi- 
nite surface,  and  there  is  no  such  thing  as  a  vessel  half  full  of 
gas.  On  the  other  hand,  if  gases  are  subjected  to  pressure,  their 
volume  may  be  indefinitely  diminished  ;  for  instance,  the  air  that 
now  fills  a  quart  vessel  may  be  compressed  into  a  pint  vessel, 
or  even  into  less  space,  if  sufficient  force  is  used.  The  com- 


18  MATTER   AND   ITS    PROPERTIES. 

pression  of  liquids  is  barely  perceptible,  even  when  the  pressure 
is  very  great. 

§  17.  Philosophy  of  the  three  states  of  matter.  —  We 
conclude  from  the  difficulty  which  we  experience  in  separating 
the  parts  of  a  solid  body,  that  the  molecular  attractive  force  in 
solids  is  very  great.  From  the  ease  with  which  we  usually 
^separate  the  parts  of  a  body  of  liquid,  we  might  conclude  that 
this  force  in  liquids  is  very  weak.  But  before  arriving  at  any 
conclusion,  it  is  necessary  to  consider  how  the  difficulty  of  sepa- 
ration of  the  parts  of  a  liquid  is  to  be  measured.  It  is  very 
easy  to  tear  off  a  portion  of  a  sheet  of  tinfoil,  but  we  should  not 
surely  regard  this  as  an  evidence  that  the  molecules  of  tin  have 
but  little  attraction  for  each  other,  for  in  tearing  such  a  body  we 
only  apply  the  force  to  a  comparatively  few  molecules  at  a  time. 
We  can  form  a  just  estimate  of  the  strength  of  molecular  attrac- 
tion only  by  attempting  to  separate  the  foil  into  two  portions  by 
such  means  as  that  the  separation  ma}7  take  place  no  sooner  at 
one  point  than  at  another.  So,  too,  it  is  very  easy  to  separate 
a  drop  of  water  into  two  portions,  but  this  is  no  measure  of  the 
attractive  forces  unless  we  take  precautions  that  we  do  not  appl}r 
the  separating  force  successively  to  different  molecules.  If  we 
succeed  in  preventing  such  a  successive  action,  and  there  are 
certain  methods  of  doing  this  more  or  less  perfectly,  we  should 
find  the  process  much  more  difficult,  —  more  so  indeed,  than  to 
produce  a  similar  change  in  many  solids.1 

There  is,  however,  a  difference  in  the  molecular  action  in 
solids  and  liquids ;  such  that,  in  the  latter  state,  the  molecular 
forces  offer  no  resistance  to  a  shaping  force,  while  in  the  former 
state,  change  of  shape  can  only  be  brought  about  by  the  appli- 
cation of  considerable  force. 

In  a  gas,  on  the  contrary,  there  is  little  attraction  between  the 
molecules ;  but  as  they  are  constantly  hitting  one  another,  and 
thereby  tending  to  drive  one  another  apart,  it  requires  an  external 
force  to  keep  them  together. 

1  The  cohesive  force  of  water  is  at  least  132  Ibs.  per  square  inch.  —  MAXWELL. 


PHILOSOPHY  OP  THE  THEEB  STATES  OF  MATTER.        19 

NOTE.  In  gases,  the  molecules  are  thought  to  be  in  motion  like  gnats 
in  the  air ;  in  liquids,  like  men  moving  through  a  crowd ;  in  solids,  the 
motion  of  each  molecule  is  like  that  of  a  man  in  a  dense  crowd  where 
it  is  almost  or  quite  impossible  to  leave  his  neighbors,  yet  he  may  turn 
around,  and  have  some  motion  from  side  to  side. 

Practically,  the  condition  of  any  portion  of  matter  depends 
upon  its  temperature  and  pressure.  (See  p.  160.)  Just  as  at 
ordinary  pressures  water  is  a  solid,  a  liquid,  or  a  gas,  according 
to  its  temperature,  so  any  substance  may  be  made  to  assume 
any  one  of  these  forms  unless  a  change  of  temperature  occasions 
a  chemical  change. 

There  are  certain  apparent  exceptions  to  the  last  statement ; 
for  example,  charcoal,  though  it  has  been  vaporized,  has  never 
been  obtained  in  a  liquid  state,  simply  because  sufficient  press- 
ure has  never  been  used.  Ice  will  change  to  a  vapor,  but  can- 
not be  melted  unless  the  pressure  exceeds  six  grams  per  square 
centimeter.  For  a  similar  reason,  iodine  and  camphor  vaporize, 
but  do  not  melt.  Alcohol  has  never  been  solidified,  or  frozen.1 
It  has  been  rendered  thick  and  pasty,  —  a  semi-solid  condition, 
—  showing  that  it  only  requires  a  little  lower  temperature  than 
any  to  which  it  has  been  exposed,  to  complete  the  solidification. 

As  regards  the  temperature  at  which  different  substances 
assume  the  different  states,  there  is  great  diversity.  Oxygen 
and  nitrogen  gases,  or  air,  —  which  is  a  mixture  of  the  two, — 
liquefy  and  solidify  only  at  extremely  low  temperatures ;  and 
then,  only  when  the  attractive  force  is  aided  by  tremendous 
pressure.  On  the  other  hand,  certain  substances,  as  quartz  and 
lime,  are  liquefied  only  by  the  most  intense  heat  generated  by  an 
electric  current.  The  facts,  summed  up,  are  as  follows :  no  one 
of  the  three  states  of  matter,  solid,  liquid,  or  gaseous,  is  peculiar 
to  any  substance;  the  state  that  a  substance  assumes  depends 
solely  on  its  temperature  and  pressure;  so  that  every  solid  may  be 
regarded  as  simply  matter  in  a  frozen  state,  every  liquid  as  mat- 
ter in  a  melted  state,  and  every  gas  as  matter  in  a  state  of  vapor. 

1  Since  this  statement  was  written  alcohol  has  been  frozen  at  about  —130°  C. 


20  MATTER  AND  ITS   PROPERTIES. 

Every  liquid  has  been  solidified  and  volatilized,  and  every  gas 
has  been  liquefied  and  solidified.  Air  was  one  of  the  last  of  the 
gases  to  surrender  its  reputation  of  being  a  "  permanent  gas." 
Not  till  the  year  1878  was  it  reduced  to  lumps.  We  may  predict 
the  future  of  our  globe.  If  its  heat  increases  sufficiently,  the 
whole  world  will  become  a  thin  gas.  If  its  heat  diminishes  indefi- 
nitely, all  earth  and  air  will  become  a  solid  mass. 

III.     PHENOMENA  OF  ATTRACTION. 

ACCORDING  to  the  circumstances  under  which  attraction  acts, 
we  have  the  various  phenomena  called  gravitation,  cohesion,  ad- 
hesion, capillarity,  chemism,  and  magnetism.  Sometimes  these 
terms  are  used  as  names  of  the  unknown  forces  that  cause  the 
phenomena. 

§  18.  Gravitation.  —  That  attraction  which  is  exerted  on  all 
matter,  at  all  distances,  is  called  gravitation.  Gravitation  is 
universal,  that  is,  every  molecule  of  matter  attracts  every  other 
molecule  of  matter  in  the  universe.  The  whole  force  with 
which  two  bodies  attract  one  another  is  the  sum  of  the  attrac- 
tions of  their  molecules,  and  depends  upon  the  number  of  mole- 
cules the  two  bodies  collectively  contain,  and  the  mass  of  each 
molecule.  The  whole  attraction  between  an  apple  and  the  earth 
is  equal  to  the  sum  of  the  attractions  between  every  molecule 
in  the  apple  and  every  molecule  in  the  earth. 

§19.  Weight.  —  It  is  scarcely  necessary  to  state,  that  what 
is  understood  by  the  weight  of  a  body  is  the  mutual  attraction 
between  it  and  the  earth.  The  term  mass  is  equivalent  to  the 
expression  quantity  of  matter.  It  follows,  then,  that  weight  is 
proportional  to  mass.  Why  do  we  weigh  articles  of  trade,  such 
as  sugar  and  tea? 

§  20.  Does  the  apple  attract  the  earth  with  as  much 
force  as  the  earth  attracts  the  apple?  —  Let  us  examine  this 
question.  First  assume  that  the  molecules  of  the  apple  and  the  earth 
have  equal  masses,  i.e.,  are  homogeneous;  then  the  attraction  of  any 


LAW   OF   GRAVITATION.  21 

molecule  in  the  apple  for  any  molecule  in  the  earth  is  equal  to  the 
attraction  of  any  molecule  in  the  earth  for  any  molecule  in  the  apple. 
That  is,  if  the  earth  and  the  apple  consisted  each  of  a  single  like  mole- 
cule, their  attraction  for  each  other  would  be  equal.  Now  suppose 
that  the  apple  contains  two  and  the  earth  five  such  molecules.  Let 
the  force  with  which  one  molecule  attracts  another  be  represented  by  n. 
Now,  each  molecule  of  the  apple  attracts  the  five  molecules  in  the  earth 
with  a  force  of  5  n ;  the  two  molecules  in  the  apple  would  attract  the 
earth  with  a  force  of  10  n.  On  the  other  hand,  each  molecule  of  the 
earth  attracts  the  molecules  of  the  apple  with  a  force  of  2n,  and  the 
five  molecules  in  the  earth  would  attract  the  apple  with  a  force  of 
10  n.  It  is  obvious  that  the  same  course  of  reasoning  will  apply  in 
case  the  attraction  is  between  two  molecules  whose  masses  differ, 
and  consequently  between  all  bodies  of  whatever  mass  or  substance. 
Hence  a  body  of  small  mass  attracts  a  body  of  large  mass  as  strongly 
as  the  latter  attracts  the  former. 

If  the  apple  attracts  the  earth  as  strongly  as  the  earth  attracts  the 
apple,  why  does  not  the  earth  rise  to  meet  the  apple  ?  Let  us  examine 
a  similar  case.  Suppose  that  a  man  in  a  boat  pulls  on  a  rope  attached 
to  a  ship.  His  pulling  draws  the  boat  to  the  ship,  but  the  ship  does 
not  appear  to  move.  But  if  five  hundred  men,  in  as  many  boats,  pulled 
together,  the  ship  would  be  seen  to  move.  Did  the  one  man  produce 
no  motion  ?  If  so,  then  would  the  five  hundred  men  produce  no  mo- 
tion, since  five  hundred  times  nothing  is  nothing?  Yes,  the  apple 
moves  the  earth  as  surely  as  the  earth  moves  the  apple ;  but  the  apple 
has  more  to  move,  and,  consequently,  it  moves  the  earth  a  distance  as 
many  times  less  than  it  is  moved  by  the  earth,  as  the  quantity  of  mat- 
ter in  the  earth  is  times  the  quantity  of  matter  in  the  apple.  The  re- 
spective distances  the  two  bodies  move  vary  inversely  as  their  masses. 

§  21.  The  force  of  gravity  varies  with  the  distance 
from  the  center.  —  Observations  made  in  various  ways  show 
that  the  force  of  gravity  varies  over  the  surface  of  the  earth.  It 
can  be  proved  by  geometrical  methods  that  a  sphere  or  a  spheroid 
acts  upon  a  molecule  without  it  as  though  all  its  attractive  force 
were  concentrated  at  its  center.  Now  it  is  found  that  the  nearer 
an  object  without  the  earth's  surface  is  to  the  center  of  the  earth 
the  greater  is  the  force  of  gravity.  The  polar  diameter  of  the 
^arth  is  about  26  miles  less  than  its  equatorial  diameter,  and, 
consequently,  the  distance  from  the  center  to  the  surface  at  the 


22  MATTEE   AND   ITS   PROPERTIES. 

poles  is  13  miles  less  than  to  the  surface  at  the  equator.  This 
considerable  difference  in  distance  from  the  center  occasions  an 
appreciable  difference  between  the  weight  of  a  body  (having  any 
considerable  mass)  at  the  equator  and  at  the  poles ;  and,  since 
the  distance  of  the  surface  from  the  center  constantly  increases 
as  we  go  from  the  poles  toward  the  equator,  the  weight  of  all 
objects  transported  from  the  poles  toward  the  equator  constantly 
diminishes. 

It  is  obvious  that  any  object  raised  above  the  earth's  surface, 
as  in  a  balloon,  must  weigh  less  than  at  the  surface  of  the  earth. 
But  the  hights  with  which  we  commonly  have  to  deal  in  our  ex- 
periments are  so  small  in  comparison  with  the  earth's  radius,  that 
the  differences  in  weight  due  to  differences  in  hight  at  a  given 
place  can  scarcely  be  detected  by  most  delicate  tests. 

The  statement  that  "  weight  is  proportional  to  mass"  (§19) 
must,  therefore,  be  restricted  to  a  comparison  of  masses  at  the 
same  place  and  at  the  same  altitude  only.  The  propriety  of 
making  a  distinction  between  the  terms  mass  and  weight  is 
now  apparent,  as  the  former  implies  that  which  does  not  change 
when  a  body  is  transferred  from  place  to  place,  while  the 
latter  may  change. 

If  the  earth  were  of  uniform  dens%,  bodies  carried  below  its 
surface  would  lose  in  weight  as  the  distance  below  the  surface 
increases.  At  one-fourth  the  distance  to  the  center  there  would 
be  a  loss  of  one-fourth  the  weight.  At  one-half  the  distance 
the  weight  would  be  one-half;  and  at  the  center  nothing.  Is 
weight  an  essential  property  of  matter  ?  State  certain  condi- 
tions on  which  a  body  would  have  no  weight. 

The  terms  up  and  down  are  derived  from  the  attraction  be- 
tween the  earth  and  terrestrial  objects.  Down  is  toward  the 
center  of  the  earth,  or  it  is  the  direction  in  which  a  body  falls  or 
tends  to  move  in  consequence  of  gravitation.  Up  is  the  oppo- 
site direction.  It  is  apparent  that  the  up  and  down  of  one 
place  cannot  correspond  with  the  up  and  down  of  any  other 
place. 


COHESION.  •  23 

QUESTIONS. 

1.  If  an  iron  pound-weight  and  a  pound  of  sugar  were  balanced  with 
ordinary  scales  at  the  equator,  and  transported  to  one  of  the  poles  of 
the  earth,  would  they  cease  to  balance  each  other  ? 

2.  If  the  same  quantity  of  sugar  be  suspended  from  a  spring-balance 
at  the  pole,  will  this  instrument  indicate  just  a  pound,  more  or  less  ? 

3.  Imagine  yourself  at  the  center  of  the  earth.     In  what  direction 
must  you  turn  your  face  in  order  to  look  up  ? 

4.  Imagine  a  person  at  one  of  the  poles,  and  another  at  the  equa- 
tor, to  be  looking  down  upon  you  at  the  center  of  the  earth.     Would 
they  both  look  in  the  same  direction  ? 

5.  Draw  a  circle  to  represent  the  earth,  and  two  lines  to  represent 
the  direction  in  which  the  two  persons  would  look. 

6.  What  is  the  origin  of  "  water-power"  ? 

7.  What  is  the  cause  of  tides  ? 

8.  Which  is  more  difficult,  to  ascend  or  descend  a  hill,  and  why  ? 

9.  The  earth  has  about  81  times  as  much  matter  in  it  as  the  moon. 
At  which  body  would  you  weigh  more  ? 

10.  Is  there  a  place  between  the  two  bodies  at  which  you  would 
weigh  nothing  ?    If  so,  why  ? 

11.  How  far  does  the  earth's  attraction  extend? 

12.  Which  would  you  prefer,  a  pound  of  gold  weighed  with  a  spring- 
balance  at  the  surface  of  the  earth,  or  a  pound  weighed  3,000,000m 
below  the  surface  ? 


§  22.  Cohesion.  — That  attraction  which  holds  the  molecules 
of  the  same  substance  together,  so  as  to  form  larger  bodies,  is 
called  cohesion.  It  is  the  force  that  prevents  our  bodies,  and 
all  bodies,  from  falling  down  into  a  mass  of  dust.  It  is  that 
force  which  resists  a  force  tending  to  break  or  crush  a  body.  It 
is  greatest  in  solids,  usually  less  in  liquids,  and  nothing  in  gases. 
It  acts  only  at  insensible  distances,  and  is  strictly  a  molecular 
force.  When  once  the  cohesion  is  overcome,  it  is  difficult  to  force 
the  molecules  near  enough  to  one  another  for  this  force  to  become 
effective  again.  Broken  pieces  of  glass  and  crockery  cannot 
be  so  nicely  readjusted  that  they  will  hold  together.  Yet  two 
polished  surfaces  of  glass,  placed  in  contact,  will  cohere  quite 
strongly.  Or  if  the  glass  is  heated  till  it  is  soft,  or  in  a  semi- 


24  .  MATTER   AND   ITS   PROPERTIES. 

fluid  condition,  then,  by  pressure,  the  molecules  at  the  two 
surfaces  will  flow  around  one  another,  pack  themselves  closely 
together,  and  the  two  bodies  will  become  firmly  united.  This 
process  is  called  welding.  In  this  manner  iron  is  welded. 

Cohesive  force  varies  greatly  in  different  substances,  according 
to  the  variation  in  the  nature,  form,  and  arrangement  of  the 
molecules  of  which  they  are  composed.  These  modifications  of 
the  force  of  attraction  give  rise  to  certain  conditions  of  matter, 
designated  as  crystalline,  amorphous,  hard,  flexible,  elastic,  brit- 
tle, viscous,  malleable,  ductile,  and  tenacious. 

§  23.  Crystalline  and  amorphous  conditions  of  matter. 
—  If  our  vision  could  be  rendered  keen  enough  to  enable  us  to 
see  and  examine  the  molecular  structure  of  different  substances, 
to  look  into  their  bodies,  as  we  look  into  the  starry  heavens,  and 
observe  the  positions,  the  spaces,  and  the  arrangement  of  that 
unexplored  world,  there  would  undoubtedly  be  unfolded  to  us 
wonders  and  beauties  of  which  we  have  never  dreamed.  We 
should  probably  behold  an  endless  variety  of  arrangement  among 
the  molecules.  We  might  learn  why  it  is  that  the  molecule  of 
the  diamond,  of  graphite,  and  of  charcoal  being  the  same  (i.e., 
the  same  substance),  we  get,  possibly  by  different  arrangement 
and  different  behavior  of  molecular  forces,  the  hard,  transparent, 
and  brilliant  diamond  in  the  one  case,  the  soft,  opaque,  metallic- 
looking  graphite  in  another,  and  finally  the  porous,  black,  and 
shapeless  charcoal. 

Obtain  a  piece  of  mica,  or  Iceland  spar,  and  a  piece  of  chalk, 
and  attempt  to  cut  them  in  two,  by  applying  the  knife  in  differ- 
ent directions.  You  find  that  you  can  easily  cleave  the  mica  in 
one  direction,  and  obtain  a  smooth,  shining  surface.  This  is 
called  its  plane  of  cleavage.  Cut  it  in  any  other  direction,  and 
you  get  rough  and  ragged  surfaces.  The  spar  may  be  cleft 
easily  and  smoothly  in  three  directions.  But  the  chalk  may  be 
cleft  in  one  direction  as  well  as  another,  and  in  no  direction  can 
a  smooth  surface  be  obtained.  We  learn  by  these  trials  that 


CRYSTALLIZATION.  25 

matter  may  have  method  in  its  arrangement,  or  possess  definite 
structure. 

When  matter  exhibits  structure  or  method  in  its  molecular 
arrangement,  it  is  said  to  be  crystalline.  Examples  of  crys- 
talline  arrangement  are  mica,  Iceland  spar,  and  carbon  in  the 
form  of  diamond.  When  its  molecular  arrangement  is  method- 
less  or  structureless,  it  is  said  to  be  amorphous.  Examples  of 
amorphous  matter  are  chalk,  glue,  glass,  and  carbon  in  the  form 
of  charcoal. 

Experiment  1.  Pulverize  20s  of  alum,  and  dissolve  in  50ccm  of  hot 
water  ;  suspend  a  thread  in  the  solution,  and  put  it  away  where  it  can 
quietly  and  slowly  cool.  After  it  has  become  cold,  you  will  find 
attached  to  the  thread  beautiful  transparent  bodies  of  regular  shape. 
The  process  by  which  matter  in  solidifying  assumes  a  structural  con- 
dition is  called  crystallization,  and  bodies  which  have  acquired  regular 
shape  by  this  process  are  called  crystals.  Obtain  crystals  of  saltpetre, 
blue  vitriol,  and  potassium  bichromate,  by  dissolving  as  much  as  pos- 
sible of  these  substances  in  hot  water,  and  allowing  the  solutions  to 
cool,  always  slowly  and  quietly. 

Experiment  2.  Thoroughly  clean  a  piece  of  window-glass,  and  pour 
upon  it  a  hot,  concentrated  solution  (see  §  36)  of  ammonium  chloride 
or  saltpetre.  Allow  the  liquid  to  drain  off,  hold  it  up  to  the  sunlight, 
and  you  will  see  beautiful  crystals  rapidly  springing  into  existence, 
spreading  and  branching  like  vegetable  growth. 

Very  interesting  illustrations  of  cr}Tstallization  are  those  deli- 
cate lacelike  figures  which  follow  the  touch  of  frost  on  the 
window-pane.  Figure  10  represents  a  few  of  more  than  a  thou- 
sand forms  of  snowflakes  that  have  been  discovered,  resulting 
from  a  variety  of  arrangement  of  the  water  molecules. 

Nature  teems  with  crystals.  Nearly  every  kind  of  matter,  in 
passing  from  the  liquid  state  (whether  molten  or  in  solution)  to  the 
solid  state,  tends  to  assume  symmetrical  forms.  Crystallization 
is  the  rule  ;  amorphism,  the  exception.  Break  open  a  sugar-loaf, 
and  you  will  find  the  surface  fracture  composed  of  small,  shining, 
crystalline  surfaces,  You  can  scarcely  pick  up  a  stone  and  break 
it,  without  finding  the  same  crystalline  fracture.  Every  piece 


26  MATTER  AND   ITS  PROPERTIES. 

of  ice  is  a  mass  of  crystals,  so  closely  packed  together  that  the 
individuals  are  not  distinguishable. 

§  24.  Change  of  volume  by  crystallization.  —  This  tend- 
ency of  matter  to  structural  arrangement  is  not  only  very  inter- 
esting, but  very  important  in  the  arts.  It  is  very  natural  tr 

Fig.  10. 


suppose  that  the  new  arrangement  of  molecules,  when  passing 
from  the  liquid  to  the  solid  state,  should  occasion  either  an 
increase  or  diminution  in  volume.  We  are  not  surprised  when 
we  find  that  water,  in  freezing,  disregards  the  law  of  contraction 
by  cold,  and  that  the  molecules  are  not  found  so  closely  packed 


CHANGE   OF   VOLUME  BY  CRYSTALLIZATION.  27 

together,  in  the  new  and  structural  state,  as  when  under  the 
influence  of  cohesion  alone. 

The  force  exerted  by  the  molecules  in  changing  positions  is 
so  enormous  as  to  burst  the  strongest  vessels.  Hence  our  ser- 
vice-pipes are  burst  when  water  is  allowed  to  freeze  in  them. 
Huge  rocks  are  dislodged  from  their  resting-places  in  the  native 
quarry  on  the  mountain-side  by  water  getting  into  the  crevices, 
freezing,  expanding  }'ear  after  year,  and  pushing  the  rocks 
from  their  support.  Cast-iron  and  many  allo3's,  such  as  type- 
metal,  expand  on  solidif}1ng.  Such  metals  may  be  cast  in 
molds,  since,  in  expanding,  the}'  fill  all  the  minute  cavities  of 
the  mold.  Most  metals  contract  on  solidifying.  Hence  gold, 
silver,  and  copper  coins  require  to  be  stamped.  Cast-iron, 
when  broken,  exhibits  a  crystalline  fracture.  Wrought-iron, 
when  subjected  to  long-continued  jarring,  —  for  instance,  the 
axles  of  car-wheels,  and  iron  cannon,  —  becomes  very  brittle, 
and,  when  broken,  exhibits  a  very  marked  crystalline  fracture 
which  it  would  not  have  shown  before  long  use.  It  is  probable 
that  the  molecules  of  iron,  when  shaken  up  by  the  jarring,  are 
free  tj>  arrange  themselves  in  their  peculiar  method,  and  that,  in 
this  new  arrangement,  the  cohesive  force  is  weakened. 

§  25.  What  is  the  cause  of  this  almost  universal  ten- 
dency of  matter  to  crystallize  ?  —  We  have  no  absolute 
knowledge  of  the  doings  in  the  molecular  world.  But  we  have 
very  satisfactor}7  methods  of  judging.  Analogy  is  the  light  by 
which  we  must  frequently  explore  inaccessible  space.  We  de- 
termine the  laws  that  govern  large,  tangible  masses,  and  from 
these  we  infer  the  laws  that  govern  small,  intangible  bodies,  or 
molecules.  Let  us  adopt  this  method  in  attempting  to  unravel 
the  mystery  before  us. 

Experiment  1.  Take  two  cambric  needles,  and  draw  each  several 
times,  from  the  eye  to  the  point,  over  the  same  end  of  a  magnet.  Now 
suspend  each  needle  by  a  thread,  so  that  it  will  be  balanced  in  a  hori- 
zontal position.  Bring  the  eye  of  one  near  the  point  of  the  other. 
When  brought  near  enough,  they  attract  each  other.  Bring  the  point 


28  MATTER  AND  ITS  PROPERTIES. 

of  one  near  the  point  of  the  other ;  they  repel  one  another.  Bring  the 
eye  of  one  near  the  eye  of  the  other ;  they  repel  one  another.  We  thus 
discover  that  the  relation  of  these  two  needles  to  one  another  is  such, 
that  if  unlike  ends  are  brought  together  they  attract  one  another,  but 
if  like  ends  are  brought  together  they  repel  one  another.  The  opposite 
character  which  the  ends  of  the  needle  exhibit  is  called  polarity. 

Now  break  one  of  the  needles  into  two  pieces,  and  experiment  as 
before.  The  two  pieces  exhibit  the  same  polarity  that  the  two  unbroken 
needles  did.  Break  them  into  still  smaller  pieces,  and  the  smallest 
piece  that  you  can  obtain  possesses  polarity,  as  certainly  as  the  original 
needle.  Imagine  the  work  of  division  to  be  continued  till  the  molecule 
is  reached.  Is  it  too  much  to  assume  that  the  molecule  may  possess 
polarity  ? 

Experiment  2.  Next,  place  a  magnet  beneath  a  sheet  of  paper,  and 
sift  iron  filings  over  it.  The  instant  they  strike  the  paper  they  arrange 
themselves  in  lines  around  the  magnet  (see  Fig.  162,  page  221).  Gently 
tap  the  paper,  and  they  arrange  themselves  still  more  definitely.  This 
reminds  us  of  the  effect  of  jarring  on  the  car-axle  and  cannon,  where 
molecules,  once  set  in  motion,  tend  to  arrange  themselves  according  to 
some  guiding  principle.  Next,  lay  the  magnet  on  a  bed  of  iron  filings 
(see  page  214),  and  then  raise  it.  We  find  the  filings  clinging  most 
abundantly  to  the  ends,  diminishing  in  number  toward  the  middle. 

We  pass  readily  from  these  facts  to  conclusions  respecting  the  mo- 
lecular arrangement  in  the  crystal.  Only  grant  the  supposition  trtat  the 
molecule  is  endowed  with  something  similar  to  polarity,  and  we  can 
picture  to  ourselves  the  molecules,  like  the  iron  filings,  wheeling  into 
line  in  obedience  to  their  polar  forces.  Crystals  are  more  easily  cleft  in 
some  directions  than  in  others :  may  not  this  be  accounted  for  by 
supposing  that,  like  the  magnet,  the  attraction  on  some  sides  of  the 
molecule  is  greater  than  on  others  ? 

§  26.  Hardness.  —  Name  some  metal  that  you  can  scratch 
with  a  finger-nail.  See  if  you  can  scratch  a  piece  of  copper 
with  a  piece  of  lead,  and  vice  versa.  Get  as  many  specimens  as 
possible  of  the  following  substances :  talc,  chalk,  glass,  quartz, 
iron,  silver,  lead,  copper,  rock-salt,  and  marble.  Ascertain 
which  of  them  will  scratch  glass,  and  which  are  scratched  by 
glass.  What  term  do  we  employ  in  speaking  of  those  substances 
that  are  easily  scratched?  To  those  that  are  scratched  with 
difficulty?  Which  is  the  softest  metal  that  you  have  tried? 


FLEXIBILITY.  29 

i 
The  hardest?    Which  is  the  softer  metal,  iron  or  lead?    Which 

is  the  more  dense  metal  ?  Does  hardness  depend  upon  density  ? 
What  force  must  be  overcome  in  order  to  scratch  a  substance  ? 
When  will  one  substance  scratch  another  ? 

To  enable  us  to  express  degrees  of  hardness,  the  following 
table  of  reference  is  generally  adopted  :  — 

MOHR'S  SCALE  OF  HARDNESS. 

1.  Talc.  6.  Orthoclase  (Feldspar). 

2.  Gypsum  (or  Rock- Salt).  7.  Quartz. 

3.  Calcite.  8.  Topaz. 

4.  Fluor-Spar.  9.  Corundum. 

5.  Apatite.  10.  Diamond. 

By  comparing  a  given  substance  with  the  substances  in  the 
table,  its  degree  of  hardness  can  be  expressed  approximately  by 
one  of  the  numbers  used  in  the  table.  If  the  hardness  of  a  sub- 
stance is  indicated  by  the  number  4,  what  would  }rou  understand 
by  it? 

§  27.  Flexibility.  —  Such  substances  as  ma}T  be  bent,  or  admit 
of  a  hinge-like  movement  among  their 
molecules,  are  called  flexi ble.  What 
difference  have  you  noticed  in  differ- 
ent jack-knife  blades  ?  How  can  3rou 
tell  a  soft  blade  from  a  hard  blade? 

If  you  bend  a  stick,  as  in  Figure  11,  it  is  apparent  that  the 
molecules  on  the  upper  side  must  be  separated  from  each  other 
a  little  farther  than  usual,  and  that  they  must  have  slightly 
rolled  round  one  another,  while  those  on  the  under  side  must  be 
crowded  together  more  closely  than  usual.  On  the  other  hand, 
the  molecules  in  a  glass  rod  have  fixed  relative  positions  which 
will  permit  very  little  disturbance. 

§  28.  Elasticity.  —  Obtain  thin  strips  of  the  following  sub- 
stances :  rubber,  wood,  ivory,  whalebone,  steel,  brass,  copper, 


30 


MATTER   AND   ITS   PROPERTIES. 


iron,  zinc,  and  lead.  Stretch  the  piece  of  rubber.  What  change 
in  its  molecular  condition  must  occur  when  it  is  stretched? 
What  molecular  force  causes  it  to  contract  when  the  stretching- 
force  is  removed?  Compress  the  rubber.  What  change  of 
molecular  condition  takes  place  in  compression?  What  force 
causes  it  to  expand  when  the  pressure  is  removed?  Bend  each 
one  of  the  above  strips.  Note  which  completely  unbends  when 
the  force  is  removed.  Arrange  the  names  of  these  substances 
in  the  order  of  the  rapidity  and  completeness  with  which  they 
unbend. 

What  change  takes  place  among  the  molecules  on  the  concave 
side  of  the  bent  strips?  What,  among  the  molecules  on  the 
convex  side  ?  What  two  forces  are  concerned  in  the  unbending  ? 
Twist  the  cord  of  a  window-tassel.  What  causes  it  to  untwist? 
The  property  which  matter  possesses  of  recovering  its  former 
shape  and  volume,  after  having  j-ielded  to  some  force,  is  called 
elasticity.  To  what  forces  is  elasticity  due?  Does  all  mat- 
ter possess  this  property  in  the  same  degree?  Does  the  rub- 
ber possess  the  same  ability  to  unbend,  as  to  contract  after 
being  stretched?  In  what  four  ways  have  you 
tested  the  elasticity  of  substances  ?  Does  a  sub- 
stance possess  equal  power  of  recovering  its  form 
after  yielding  to  each  of  these  four  methods  of 
applying  force?  Why  are  pens  made  of  steel? 
What  moves  the  machinery  of  a  watch  ?  What 
is  the  cause  of  the  softness  of  a  hair  mattress  or 
feather-bed? 

A  common  spring-balance  used  for  weighing  cou- 
sists  of  a  steel  spring  wound  into  a  coil.  The  weight 
of  the  body  to  be  weighed  straightens  or  draws  out 
the  spring.  A  pointer  moving  over  a  plate  which  is 
divided  into  equal  parts  shows  how  much  the  spring  has  been  drawn 
out.  But  the  entire  virtue  of  this  apparatus  consists  in  the  elasticity 
of  the  spring,  or  its  power  to  recover  its  original  form  after  being 
drawn  out.  Give  other  illustrations  of  the  application  of  elasticity 
to  practical  purposes. 


Fig.  12. 


BRITTLENESS.  —  VISCOSITY.  31 

Any  alteration  in  the  form  of  a  body  due  to  the  application  of 
a  force  is  called  a  strain,  and  the  force  by  which  the  strain  is 
produced  is  called  the  stress.  A  body  which,  having  experienced 
a  strain  due  to  a  certain  stress,  completely  recovers  its  original 
condition  when  the  stress  is  removed,  is  said  to  be  perfectly 
elastic.  Liquids  and  gases  are  perfectly  elastic  (see  §  48) .  Solids 
are  perfectly  elastic  up  to  a  certain  limit,  which  varies  greatly  in 
different  substances.  If  the  stress  exceeds  a  certain  limit,  the 
form  of  the  solid  becomes  permanently  altered,  and  the  state  of 
the  body,  when  the  permanent  alteration  is  about  to  take  place, 
is  called  the  limit  of  perfect  elasticity.  In  soft  or  plastic  bodies 
this  limit  is  soon  reached.  What  is  the  result  of  overloading 
carriage  springs? 

§29.  Brittleness. — Apply  sharp  blows  with  a  hammer  to 
each  of  the  substances  whose  hardness  you  have  tested  (§  26), 
and  ascertain  which  are  the  most  easily  broken  or  pulverized. 
Observe  that  some  substances  suffer  a  permanent  change  in  form 
when  subjected  to  a  stress  which  exceeds  their  limit  of  elasticity, 
while  others  break  before  there  is  any  permanent  alteration  in 
form.  The  latter  are  said  to  be  brittle. 

§  30.  Viscosity.  —  Support  in  a  horizontal  position,  at  one 
of  its  extremities,  a  stick  of  sealing-wax,  and  suspend  from  its 
free  extremity  a  small  weight,  and  let  it  remain  in  this  condition 
several  daj's,  or  perhaps  weeks.  At  the  end  of  the  time  the 
stick  will  be  found  permanently  bent.  Had  an  attempt  been 
made  to  bend  the  stick  quickly,  it  would  have  been  found  quite 
brittle.  A  body  which,  subjected  to  a  stress  for  a  considerable 
time,  suffers  a  permanent  change  in  form,  is  said  to  be  viscous. 
Hardness  is  not  opposed  to  viscosity.  A  lump  of  pitch  may  be 
quite  hard,  and  yet  in  the  course  of  time  it  will  flatten  itself  out 
by  its  own  weight,  and  flow  down  hill  like  a  stream  of  syrup. 
Liquids  like  molasses  and  honey  are  said  to  be  viscous,  in  dis- 
tinction from  limpid  liquids  like  water  and  alcohol. 


32  MATTER   AND   ITS   PROPERTIES. 

§31.  Malleability  and  ductility.  —  Some  substances  pos- 
sess, in  the  solid  state,  a  certain  amount  of  fluidity  ;  that  is, 
their  molecules  ma}'  be  displaced  without  overcoming  their  cohe- 
sion. Place  a  piece  of  lead  on  an  anvil,  and  hammer  it.  It 
spreads  out  under  the  hammer  into  sheets,  without  being  broken, 
though  it  is  evident  that  the  molecules  have  moved  about  among 
one  another,  and  assumed  entirety  different  relative  positions. 
Heat  a  piece  of  soft  glass  tube  in  a  gas-flame,  and,  although  the 
glass  does  not  become  a  liquid,  it  behaves  very  much  like  a 
liquid,  and  can  be  drawn  out  into  very  fine  threads.  When  a 
solid  possesses  sufficient  fluidity  to  admit  of  being  drawn  out 
into  threads,  it  is  said  to  be  ductile.1  When  it  will  admit  of 
being  hammered  or  rolled  into  sheets,  it  is  said  to  be  malleable. 

As  might  be  expected,  those  substances  that  are  ductile  are  also  mal- 
leable. But  the  same  substance  does  not  usually  possess  the  two 
properties  in  an  equal  degree.  Platinum  is  the  most  ductile  metal.  It 
can  be  drawn  into  wire  finer  than  a  spider's  thread.  It  is  the  seventh 
metal  in  the  rank  of  malleability.  Gold  is  the  most  malleable  metal. 
It  can  be  hammered  into  leaves  so  thin,  that  it  would  require  300,000 
to  make  a  book  one  inch  thick.  It  ranks  next  to  platinum  in  ductility. 
Iron,  at  a  red  heat,  is  very  malleable  and  ductile.  What  metals  can 
be  drawn  into  wires  ?  What  metals  can  be  rolled  or  hammered  into 
sheets? 

§32.  Tenacity.  —  In  order  that  a  substance  may  be  ductile, 
it  is  evident  that  it  must  possess  a  strong  cohesive  force,  so  as 
to  prevent  rupture.  The  power  that  matter  possesses  of  resisting 
rupture,  b}T  a  pulling  force,  is  called  tenacity.*  A  body  may  be 
tenacious  ivithout  being  ductile,  but  it  cannot  be  ductile  ivithout 
being  tenacious.  It  is  remarkable  that  the  tenacity  of  most 
metals  is  increased  by  being  drawn  out  into  wires.  It  would 
seem,  that,  in  the  new  arrangement  which  the  molecules  assume, 
the  cohesive  force  is  stronger  than  in  the  old.  Hence  cables 
made  of  iron  wire  twisted  together,  so  as  to  form  an  iron 

1  Ductile,  draw-able.  2  Malleable,  as  it  were  mallet-able. 

8  Tenacity,  property  of  holding. 


ADHESION.  33 

rope,  are  stronger  than  iron  chains  of  equal  weight  and  length, 
and  are  much  used  instead  of  chains,  where  great  strength  is 
required. 

§33.  Adhesion.  —  Grasp  with  your  finger  a  piece  of  gold- 
leaf,  and,  honest  as  you  may  be,  it  will  stick  to  your  fingers  ;  it 
will  not  drop  off,  it  cannot  be  shaken  off,  and  to  attempt  to  pull 
it  off  is  to  increase  the  difficulty.  Dust  and  dirt  stick  to  clothing. 
Thrust  your  hand  into  water,  and  it  comes  out  wet.  You  can 
climb  a  pole,  because  your  hands  stick  to  the  pole ;  but  if  the 
pole  is  greased,  climbing  is  not  so  easy.  We  could  not  pick 
anything  up,  or  hold  anything  in  our  hands,  were  it  not  that 
these  things  stick  to  the  hands. 

Every  minute's  experience  teaches  us  that  not  only  is  there  an 
attractive  force  between  molecules  of  the  same  kind  of  matter, 
but  there  is  also  an  attractive  force  between  molecules  of  unlike 
matter.  That  force  which  causes  unlike  substances  to  cling 
together,  is  called  adhesion.  Is  adhesion  a  molar  or  a  molecular 
force  ?  How  does  it  differ  from  cohesion  ?  Why  do  not  gold 
watches,  and  other  articles  of  gold  jewelry,  appear  to  stick  to 
the  fingers?  What  keeps  nails, driven  into  wood, in  their  places? 
What  would  happen  if  all  adhesion  between  the  different  parts 
of  the  building  you  are  in  should 
be  suddenly  destroyed  ?  When  a 
liquid  sticks  to  a  solid,  what  term 
do  we  usually  employ  in  describ- 
ing the  phenomenon  ? 


Experiment  1.  Suspend  a  plate 
of  glass,  about  8cm  square,  from  one 
arm  of  a  scale-beam,  attaching  the 
threads  to  the  plate  with  sealing- 
wax.  Balance  it,  and  place  a  dish  of  water  under  the  glass,  so  that  its 
under  surface  will  just  touch  the  surface  of  the  water.  You  may 
now  add  several  grams'  weight  to  the  other  side  of  the  beam  without 
destroying  the  balance.  Finally,  the  glass  is  apparently  pulled  away 
from  the  water.  But  on  examination  you  will  find  it  wet,  so  that  you 


34  MATTER   AND   ITS   PROPERTIES. 

have  really  succeeded,  not  in  separating  the  glass  from  the  water,  but 
water  from  water.  Then  the  weight  that  you  were  obliged  to  add  does 
not  measure  the  adhesive  force  between  the  glass  and  the  water;  it 
merely  measures  the  amount  of  force  necessary  to  tear  the  liquid  apart. 
The  same  force  was  not  sufficient  to  tear  the  liquid  from  the  solid, 
hence  we  infer  that  the  adhesion  between  a  solid  and  a  liquid  may  be 
f/reater  than  the  cohesion  in  the  liquid. 

Glass  is  wet  by  water,  but  is  not  wet  by  mercury.  Is  there 
no  adhesion  between  mercury  and  glass? 

Experiment  2.  Substitute  mercury  for  water  in  the  last  experi- 
ment. As  soon  as  the  glass  touches  the  mercury  a  slight  adhesion 
occurs,  which  can  be  measured  by  the  weight  required  to  be  placed  in 
the  opposite  scale-pan  in  order  to  separate  them. 

It  is  probable  that  there  is  some  adhesion  between  all  substances 
ivhen  brought  in  contact.  If  a  liquid  adheres  to  a  solid  more 
firmly  than  the  molecules  of  the  liquid  cohere,  then  will  the  solid 
be  wet  by  the  liquid.  If  a  solid  is  not  wet  by  a  liquid,  it  is  not 
because  adhesion  is  wanting,  but  because  cohesion  in  the  liquid 
is  stronger.  That  gases  adhere  to  solids  is  proved  by  the 
phenomena  of  absorption  described  in  §  37. 

QUESTIONS. 

1.   Why  will  not  water  wet  articles  that  have  been  greased  ? 
3.   Why  is  it  difficult  to  lift  a  board  out  of  water  ? 

3.  Why  does  water  run  down  the  side  of  a  tumbler  when  it  is 
inclined,  instead  of  falling  vertically  ?    Suggest  some  method  of  pre- 
venting it. 

4.  In  what  does  the  value  of  cement,  glue,  and  mucilage  consist  ? 

5.  What  enables  you  to  leave  a  mark  with  a  pencil  or  crayon  ? 


§  34.  Capillarity.  —  Examine  the  surface  of  water  in  a  goblet. 
You  find  the  surface  level,  as  in  A  (Fig.  14),  except  around  the 
edge  next  the  glass,  where  the  water  is  curved  upward  so  as 
to  resemble  the  interior  surface  of  a  watch  crystal.  Mercury 
placed  in  a  goblet  (B)  has  its  edge  turned  downward,  resembling 
the  exterior  surface  of  a  watch  crystal.  This  seems  to  indicate 


CAPILLARITY. 


35 


a  repulsion  between  mercury  and  glass.     But  a  previous  experi- 
ment (page  34)  has  shown  that,  instead  of  repulsion,  there  is  a 
slight  adhesion  between 
these  substances.  " 

Pour  any  liquid  on  a 
level  surface  which  it 
does  not  wet,  —  e.g., 
water  on  paraffine  or 
wax,  or  mercury  on 
glass.  It  spreads  itself 
over  the  surface,  but  the 
edges  are  everywhere 
rounded  or  turned  down 
like  the  edges  of  mercury  in  a  goblet.  Surely  these  rounded 
edges  are  not  caused  by  the  repulsion  of  the  sides  of  a  vessel. 
The  edges  of  all  liquids  will  be  turned  down  unless  the  adhesion 
between  them  and  the  sides  of  the  vessels  exceeds  the  cohesion 
in  the  liquid.  The  glass  does  not  cause  the  turning  down  of 
the  surface  of  mercury  in  the  goblet,  —  its  tendenc}r  is  rather  to 
prevent  it. 

Thrust  vertically  two  plates  of  glass  into  water,  and  gradu- 
ally bring  the  surfaces  near  each  other.  Soon  the  water  rises 
between  the  plates,  and  rises  higher  as  the  plates  are  brought 
nearer.  Thrust  a  glass  tube  of  very  fine  bore  into  water ;  the 
attraction  within  it,  on  all  sides,  will  raise  the  water  to  twice  the 
hight  it  would  reach  when  between  two  palates  whose  distance 
apart  is  equal  to  the  diameter  of  the  bore  of  the  tube.  Thrust 
a  tube  of  the  same  bore  into  alcohol ;  this  liquid  rises  in  the 
tube,  but  not  so  high  as  water.  The  surfaces  of  both  the 
water  and  the  alcohol  are  concave.  If  the  tube  is  placed 
in  mercury,  the  opposite  phenomena  occur :  the  mercury  is 
depressed,  and  its  surface  is  convex.1  Both  ascension  and 

1  The  scope  of  this  book  will  not  admit  of  an  explanation  of  the  phenomena  of 
capillarity.  The  student  can  find  a  lucid  treatment  of  this  subject  in  Maxwell's  "Theory 
of  Heat;"  pp.  260-274;  also  under  "  Capillary  action,"  Encyclopaedia  Britannica. 


36  MATTER  AND  ITS   PROPERTIES. 

depression  diminish  as  the  temperature  increases,  being  greatest 
at  the  freezing  point  of  the  given  liquid,  and  least  at  its  boiling 
point.  (Regarding  heat  as  a  repellent  force,  can  you  give  any 
reason  why  the  ascension  should  be  less  at  high  than  at  low 
temperatures?)  Inasmuch  as  the  phenomena  are  best  shown 
in  tubes  having  bores  of  the  size  of  hairs,  they  are  in  such 
cases  called  capillary1  phenomena,  and  the  tubes  are  called 
capillary  tubes. 

The  phenomena  of  capillary  action  are  well  shown  by  placing 

various  liquids  in  U-shaped   glass 
tubes,  having  one  arm  reduced  to  a 
capillary  size,  as  A  and  B  in  Figure 
15.   Mercury  poured  into  A  assumes 
convex  surfaces  in  both  arms,  but 
does  not  rise  so  high  in  the  small 
arm  as  it  stands  in  the  large  arm. 
Pour  water  into  B,  and  all  the  phe- 
nomena are  reversed.     C  is  a  glass 
tube  containing  water  and  mercury, 
and  showing  the  shapes  that  the  surfaces  of  the  two  liquids  take. 
Generalizing  the  above  facts,  we  have  the  four  laws  of  capil- 
lary action  :  — 
I.   Liquids  rise  in  tubes  when  they  wet  them,  and  are  depressed 

when  they  do  not. 

II.    The  ascension  or  depression  varies  inversely  as2  the  diameter 
of  the  bore. 

III.  The  ascension  and  depression  vary  with  2  the  nature  of  the 

substances  employed. 

IV.  The  ascension  or  depression  varies  inversely  with  the  tem- 

perature. 

Illustrations  of  capillary  action  are  abundant.  It  feeds  the 
lamp-flame  with  oil.  It  wets  the  whole  towel,  if  one  end  is  left 
for  a  time  in  a  basin  of  water.  It  draws  water  into  wood,  and 
causes  it  to  swell  with  a  force  sufficient  to  split  rocks,  and  to 
raise  large  weights.  How  does  a  little  water  in  a  wooden  tub 
prevent  its  falling  to  pieces  ? 

1  Capillary,  hair-like.  2  Observe  that  throughout  this  treatise  the  word  as  expresses 
an  exact  proportion.  When  there  is  not  an  exact  proportion,  the  word  with  is  used. 


.i  ^vL*Jk,L-v 


SOLUTION  OF  SOLIDS.  37 

§35.  Other  molecular  phenomena.  —  Besides  the  phe- 
nomena we  have  just  studied,  there  are  a  great  many  others 
depending  in  part  on  molecular  attraction,  but  much  more  on  the 
molecular  motions,  of  which  we  learned  in  §  5,  page  6.  Many 
of  them  are  quite  familiar  and  important ;  but  the  explanation, 
even  when  it  can  be  given,  is  usually  complicated  and  incom- 
plete. The  principal  names  given  these  phenomena  are  solution, 
absorption,  and  diffusion. 

Su^f 

§  36.  Solution  of  solids  —  depends  mainly  on  molecular 
attraction.  Hold  a  lump  of  sugar  so  that  it  will  just  touch  the 
surface  of  water.  Soon  water  is  drawn  up  into  the  pores  of  the 
lump  by  capillary  action,  and  the  whole  lump,  including  the 
part  not  submerged,  becomes  moist.  Next  you  discover  that 
the  lump  becomes  smaller,  and  slowly  disappears  in  the  water. 

When  a  solid  becomes  diffused  through  a  liquid,  it  is  said  to 
be  dissolved.  The  dissolving  liquid  is  called  a  solvent,  and  the 
resulting  liquid  is  called  a  solution.  A  liquid  will  dissolve  a 
solid,  only  when  the  adhesion  between  them  is  greater  than  the 
cohesion  in  the  solid.  A  liquid  always  dissolves  a  solid  more 
rapidly  at  first,  less  rapidly  as  the  adhesion  becomes  more  nearly 
satisfied  ;  and  when  it  is  completely  satisfied,  or  is  balanced  by 
the  cohesion  in  the  solid,  the  liquid  will  dissolve  no  more  of  the 
solid,  and  the  solution  is  said  to  be  saturated.  When  a  solution 
will  take  much  more  of  a  solid,  it  is  said  to  be  dilute  ;  and 
concentrated,  when  it  will  take  little  or  no  more. 

If  the  solid  be  first  pulverized,  the  liquid  has  more  surface  on 
which  to  act,  and  the  solid  is  dissolved  much  more  rapidly. 
Heat  generally  weakens  cohesion  more  than  it  weakens  adhesion ; 
hence,  with  few  exceptions,  hot  liquids  dissolve  solids  more 
rapidly  and  in  greater  quantities  than  cold  liquids.  Boiling 
water  dissolves  three  times  as  much  alum  as  cold  water ;  conse- 
quently, when  a  hot  saturated  solution  of  alum  is  allowed  to 
cool,  at  least  two-thirds  of  the  alum  must  be  restored  to  the 
solid  state  (see  Exp.  1,  page  25),  while  one-third,  or  the  amount 


38  MATTER   AND  ITS   PROPERTIES. 

that  the  cold  liquid  is  capable  of  dissolving,  remains  in  solution. 
The  remaining  solution  is  called  the  mother-liquor.  Lime,  and 
a  few  other  substances,  are  dissolved  better  in  cold  water. 
Crystals  of  such  substances  are  only  obtained  by  gradual  evap- 
oration of  the  solvent. 

Water  is  the  great  solvent.  When  we  speak  of  the  solubility  of  a 
substance,  water  is  always  UDderstood  to  be  the  solvent,  unless  sonic 
other  liquid  is  specified.  Why  is  it  fortunate  that  water  is  so  good  a 
solvent?  Name  substances  that  water  does  not  dissolve.  Of  the 
many  substances  insoluble  in  water,  some,  as  phosphorus,  gums,  and 
resin,  find  a  solvent  in  alcohol ;  sulphur,  in  bi-sulphide  of  carbon  ;  lead, 
in  mercury;  and  fats,  in  ether  or  benzine.  Would  you  wash  var- 
nished furniture  with  alcohol?  How  are  grease-spots  removed  from 
clothing? 

§  37.  Absorption  of  gases  by  solids  —  depends  mainly  on 
molecular  attraction,  and  is  generally  superficial.  Certain  solids 
possess  so  strong  an  attraction  for  gases  that  the}T  not  only  draw 
the  gases  into  the  small  cavities  or  holes  within  them,  but  greatly 
condense  them  there.  It  should  be  carefully  noted  that  the 
attraction  in  this  case  is  generalty  between  the  gases  and  the 
surfaces  of  cavities,  and  is  hence  called  superficial,  in  dis- 
tinction from  intermolecular  attraction,  which  is  the  name  given 
to  the  phenomenon  when  gases  are  taken  into  the  pores  of  a 
body. 

Freshly-burned  charcoal  placed  in  dry  air,  may,  in  a  few  days, 
have  its  weight  increased  one-fiftieth  in  consequence  of  the  air 
that  it  absorbs.  (Has  air  weight?)  The  attraction  of  charcoal 
for  noxious  gases  is  especially  great,  making  it  very  efficient 
in  cleansing  the  air  in  hospitals,  and  in  removing  noxious 
odors  from  putrid  animal  and  vegetable  matter  by  absorbing  the 
foul  gases  that  are  generated.  It  does  not  check  decay,  but 
rather  hastens  it.  A  rat,  which  had  been  buried  in  charcoal 
dust,  was  uncovered  at  the  end  of  a  month  ;  nothing  visible  was 
left  but  the  hair  and  bones,  yet  no  bad  odor  was  perceptible. 
Why  do  farmers  mix  muck  with  manures  ? 


FREE  DIFFUSION  OF  LIQUIDS.  39 

§38.  Absorption  of  gases  by  liquids  —  depends  on  molec- 
ular attraction  and  motion,  and  is  intermodular.  Water,  at  a 
temperature  of  0°  Cen.,  is  capable  of  condensing  in  its  pores 
six  hundred  times  its  own  bulk  of  ammonia  gas.  Water  thus 
charged  with  this  gas  is  called  "  ammonia  water."  The  amount 
of  gas  that  a  liquid  will  absorb  is  increased  by  pressure.  "  Soda 
water "  is  simply  water  saturated  with  carbonic-acid  gas  under 
great  pressure ;  it  contains  no  soda.  When  the  pressure  is 
removed,  a  large  part  of  the  gas  escapes,  causing  efferves- 
cence. 

§  39.  Free  diffusion  of  liquids  —  depends  mainly  on  mo- 
tion.—  Experiment  1.  Into  a  test-tube  containing  20ccm  of  water, 
pour  about  2ccmof  olive-oil,  and  shake.  By  shaking,  the  oil  becomes 
divided  into  small  particles,  which  give  the  water  an  opaque,  milky- 
white  appearance,  but  it  is  not  separated  into  its  molecules.  After 
standing  for  a  few  minutes,  the  oil  almost  completely  separates  from 
the  water,  and  rises  to  the  top. 

Experiment  2.  Partially  fill  a  glass  jar  (Fig.  16)  with  water.  Then 
introduce  beneath  the  water,  by  means  of  a  long  tunnel,  a  concentrated 
solution  of  sulphate  of  copper.  The  lighter  liquid  Fi  1(J 

rests  upon  the  heavier,  and  the  line  of  separation 
between  the  two  liquids  is  at  first  distinctly  marked. 
But  in  the  course  of  days  or  weeks  this  line  will 
gradually  become  obliterated,  the  heavier  blue  liquid 
will  gradually  rise,  and  the  lighter  colorless  liquid  will 
descend,  till  they  become  thoroughly  mixed. 

Experiment  3.  Take  about  lccm  of  bisulphide  of 
carbon,  color  it  by  dropping  into  it  a  small  particle 
of  iodine,  and  pour  this  colored  solution  into  a  test- 
tube  nearly  filled  with  water.  The  colored  liquid, 
being  heavier  than  the  water,  sinks  directly  to  the 
bottom,  and  shows  no  tendency  to  mix  with  the  water.  But,  in  the 
course  of  time,  you  discover  that  the  colored  liquid  diminishes  in 
quantity,  and  finally  disappears.  The  peculiar  odor  of  this  substance 
which  pervades  the  air  in  the  vicinity  shows  that  a  considerable  por- 
tion has  evaporated.  But  it  must  have  worked  its  way  gradually 
through  the  water  above  it. 


40 


MATTER   AND   ITS  PROPERTIES. 


Fig.  17. 


If,  during  the  operation  of  diffusion  in  the  last  two  experi- 
ments, you  examine  the  liquid  with  a  microscope,  you  will  not 
be  able  to  trace  any  currents ;  hence  the  motion  of  liquids  in 
diffusion  is  not  in  mass,  but  by  molecules,  —  a  kind  of  inter- 
molecular  motion.  We  learn  that  some  liquids,  even  when 
stirred  together,  will  not  remain  mixed;  while  others,  whose 
densities  are  very  different,  when  merely  placed  in  contact  with 
each  other,  slowly  mix  of  themselves. 

§  40.  Diffusion  of  liquids  through  porous  partitions. 
—  Osmose.  —  Dialysis.  —  Very  complex.  —  Experiment.  Cut 
off  the  bottom  of  a  conical-shaped  bottle '  (or,  better,  use  a  glass  tun- 
nel or  lamp-chinm  -y) ;  fit  to  the  ueck  of  the 
bottle  a  cork,  having  a  glass  tube  passing 
through  it  (Fig.  17).  Tic  tightly  over  the  bot- 
tom a  piece  of  gold-beater's  skin  or  parch- 
ment paper.  Fill  the  bottle  with  a  concen- 
trated solution  of  sulphate  of  copper,  and 
press  the  cork  into  the  bottle  so  that  the  liquid 
will  stand  a  little  way  up  the  tube,  say  at  a. 
Now  suspend  the  apparatus  in  a  vessel  of 
water,  so  that  the  bottom  may  be  covered. 
In  less  than  an  hour  it  will  be  found  that  the 
liquid  has  risen  in  the  tube,  showing  that 
water  must  have  passed  through  the  septum,2 
and  mixed  with  the  solution.  Examine  the 
water  in  the  outer  vessel,  and  you  will  find 
that  it  is  slightly  tinged  with  the  blue  vitriol, 
showing  that  some  of  the  solution  has  also 
passed  through  the  septum.  But  the  liquid 
has  risen  in  the  tube,  showing  that  more  of 
the  water  than  of  the  solution  has  passed 
through  the  septum. 

When  liquids  or  gases  force  their  way 
through  porous  septa,  and  mix  with  each  other,  the  diffusion  is 
called  osmose.3  To  distinguish  the  two  opposite  currents,  the 
flow  of  the  liquid  or  gas  towards  that  which  increases  in  volume 

i  See  Appendix,  Section  B.          2  Septum,  partition.          »  Osmose,  impulse. 


FREE  DIFFUSION  OF  GASES. 


41 


Fig.  18. 


is  called  endosmose,1  and  the  opposite  current  is  called  exos- 
mose.% 

It  is  found  that  crystallizable  substances  are  the  best  subjects 
of  osmose,  while  those  which  are  usually  amorphous,  such  as 
gelatine  and  gummy  substances,  are  very  little .  inclined  to 
osmose.  Those  substances  that  pass  readily  through  septa 
are  called  crystalloids;*  those  that  do  not  are  called  colloids.* 

The  principle  of  unequal  diff  usibility  of  liquids  through  septa 
finds  important  application  in  chemical 
and  pharmaceutical  laboratories.  For 
example,  from  a  rod  (Fig.  18)  is  sus- 
pended a  glass  vessel  having  a  bottom 
of  parchment  paper.  Such  a  vessel  is 
called  a  dialyzer.  In  the  dialyzer  is 
placed,  for  instance,  the  liquid  contents 
of  the  stomach  or  intestines  of  a  dead 
animal,  suspected  of  containing  some 
poison,  and  the  vessel  is  floated  in  a 
vessel  of  water.  If  either  arsenic  or 
strychnine  is  present  it  will  separate  from 
the  albuminous  matter  hi  the  food,  and 
pass  through  the  septum  into  the  water.  The  process  of  sep- 
arating mixed  liquids  by  osmose  is  called  dialysis. 


§  41.  Free  diffusion  of  gases  —  depends  almost  wholly  on 
molecular  motion.  —  Experiment.  Fill  a  test-tube  with  oxygen  gas, 
and  thrust  in  a  lighted  splinter;  the  splinter  burns  much  more  rapidly 
than  in  the  air.  Fill  another  tube  with  hydrogen  gas,  and  keep  the 
tube  inverted  (for,  this  gas  being  about  sixteen  times  lighter  than  air, 
there  will  be  no  danger  of  its  falling  out) .  Thrust  in  a  lighted  splinter ; 
the  gas  takes  fire,  and  burns  with  a  pale  flame  at  the  mouth  of  the  tube. 
Next  fill  one  tube  with  oxygen  and  the  other  with  hydrogen  gas,  and 
place  the  mouth  of  the  latter  over  the  mouth  of  the  former,  as  in  Fig- 
ure 19.  In  about  a  minute  apply  a  lighted  splinter  to  the  mouth  of  each 


1  Endosmose,  inward  impulse. 

2  Exosmose,  outward  impulse. 


»  Crystalloid,  like  crystal. 
*  Colloid,  like  gum. 


42 


MATTER   AND  ITS  PROPERTIES. 


Fia:.  19. 


tube  (let  the  mouth  of  each  tube  be  freely  open  to  prevent  accident)  ; 
a  slight  explosion  takes  place  in  each  instance.  It  is  apparent  that 
although  the  oxygen  gas  is  sixteen  times  heavier  than  the  hydrogen, 
some  of  it  has  risen  into  the  upper  tube,  while  some  of  the  lighter 
hydrogen  has  descended  into  the  lower  tube,  and  the  two  gases  have 
become  diffused. 

Many  pairs  of  liquids  do  not  diffuse  into  each  other,  but  every 
gas  diffuses  into  every  other  gas,  and  it  is  impossible  to  prevent  two 
gases  from  mixing  when  placed  in  contact. 
(It  is  thought  best  to  introduce  the  subject  of 
diffusion  of  liquids  and  gases  in  this  place, 
though  it  has  little  or  no  connection  with  the 
subject  of  adhesion.  The  explanation  of 
diffusion  must  be  deferred  to  its  proper  place 
in  the  chapter  on  Heat,  page  158.) 

In  consequence  of  this  universal  tendency  to 
diffusion,  gases  will  not  remain  separated,  —  i.e., 
a  lighter  resting  upon  a  heavier,  as  oil  rests  upon 
water.  This  is  of  immense  importance  in  the 
economy  of  nature.  The  largest  portion  of  our 
atmosphere  consists  of  a  mixture  of  oxygen  and 
nitrogen  gases.  There  are  always  present  also 
small  quantities  of  other  gases,  such  as  carbonic- 
acid  gas,  ammonia  gas,  and  various  other  gases, 
which  are  generated  by  the  decomposition  of 
organic  matter.  These  gases,  obedient  to  gravity 
alone,  would  arrange  themselves  according  to 
their  weight,  —  carbonic-acid  gas  at  the  bottom, 
or  next  the  earth,  followed  respectively  by  oxy- 
gen, nitrogen,  ammonia,  and  other  gases.  Neither  animal  nor  vegetable 
life  could  exist  in  this  state  of  things.  But,  in  consequence  of  their 
diffusibility,  they  are  found  intimately  mixed,  and  in  the  same  relative 
proportions,  whether  in  the  valley  or  on  the  highest  mountain  peak. 


§  42.  Diffusion  of  gases  through  porous  partitions  — 
depends  on  the  size  of  molecules,  size  of  pores,  and  on  molecular 
motion;  very  complex. 


DIFFUSION  OF  GASES.  43 

Experiment.  Take  a  thin,  unglazed  earthen  cup,  such  as  is  used  in 
Bunsen's  battery  (page  190) ,  and  plug  up  the  open 
end  with  a  cork  through  which  extends  a  glass 
tube.  Place  the  exposed  end  of  the  tube  in  a  cup 
of  colored  water.  Lower  a  glass  jar,  filled  with 
hydrogen  or  coal-gas,  over  the  porous  cup,  as  in 
Figure  20.  Instantly  air  is  forced  down  through 
the  tube,  and  escapes  in  bubbles  from  the  colored 
liquid.  The  gas  in  the  larger  vessel  forces  its  way 
through  the  pores  of  the  cup,  diffuses  itself  in  the 
air  contained  in  it,  and  causes  an  unusual  pressure 
on  the  colored  liquid,  as  is  evinced  by  the  air  that 
is  forced  out  through  it.  In  a  minute  remove  the 
glass  jar.  The  hydrogen  now  escapes  through  the 
sides  of  the  cup,  and  mixes  with  the  air  on  the  out- 
side ;  a  partial  vacuum  is  formed  in  the  cup,  and 
water  rises  in  the  tube.  In  both  cases  air  passed 
through  the  sides  of  the  porous  cup,  but  the  influx 
and  efflux  of  hydrogen  was  much  more  rapid. 

An  interesting  modification  of  this  apparatus  is  the  diffusion  foun- 
tain (Fig.  21).  By  passing  the  glass  tube  of  the  porous  cup  through 
the  cork  of  a  tightly-stopped  vessel,  and  hav-  Fi  21 

ing  another  glass  tube  pass  through  another 
perforation  in  the  same  cork,  water  is  forced 
out  in  a  jet  several  feet  in  hight,  when  the 
hydrogen  jar  is  held  over  the  porous  cup. 

Children  well  understand  that  toy  balloons, 
which  are  made  of  collodion  and  filled  with 
coal-gas,  collapse  in  a  few  hours  after  they  are 
inflated.  This  is  caused  by  the  escape  of  the 
gas  by  osmose.  Nature  furnishes  an  illustra- 
tion of  osmose  of  gases  in  respiration.  In  the 
lungs  the  blood  is  separated  from  the  air  by 
the  thin,  membranous  walls  of  the  veins. 
Carbonic-acid  gas  escapes  from  the  blood  through  these  septa,  and 
oxygen  gas  enters  the  blood  through  the  same  septa. 


CHAPTER    II. 
DYNAMICS. 


IV.     DYNAMICS   OF  FLUIDS. 

§  43.  Equilibrium,  pressure,  and  tension.  —  That  branch 
of  science  which  treats  of  force  and  the  motions  it  produces  is 
called  dynamics.  It  has  been  shown  that  force  may  act  on  a 
body  to  produce  motion  or  rest ;  also  that  two  or  more  forces 
may  so  act  on  a  body  as  to  neutralize  each  other's  effect.  In 
the  latter  case,  the  body  continues  in  the  same  condition,  either 
of  motion  or  rest,  as  if  it  were  independent  of  the  action  of  the 
forces,  and  is  said  to  be  in  equilibrium,1  and  the  forces  acting 
on  it  are  also  said  to  be  in  equilibrium.  Inasmuch  as  no  body 
is  ever  free  from  the  action  of  force,  it  must  be  that  a  body  at 
rest  is  in  a  state  of  equilibrium. 

If  any  portion  of  a  force  is  not  effective  in  producing  motion, 
—  i.e.,  if  part  or  all  of  it  is  exerted  against  other  forces,  — there 
may  result  what  is  called  a  pressure  on  the  body  ;  as  when  we 
push  on  a  wall  or  on  a  heavy  sled  moving  over  the  ice,  or  a 
book  presses  the  table.  The  same  force  which  causes  a  body  to 
fall  when  unsupported,  causes  it  to  press  on  any  obstacle  which 
prevents  it  from  falling.  Or,  if  the  force  is  exerted  on  a  body 
in  which  the  molecular  attraction  is  strong,  —  i.e.,  on  a  solid,  — 
we  may  have  a  pull  or  tension,  as  when  we  hang  in  a  swing,  or 
hang  a  stone  from  a  rubber  band.  If  the  body  under  the  influ- 
ence of  a  force  maintains  a  uniform  velocity,  we  may  measure 
the  force  by  the  pressure  (or  tension)  exerted,' or  may  measure 
the  pressure  by  the  amount  of  the  force,  whichever  may  be  more 
convenient.  The  case  of  uniform  velocity  includes  the  case  of  rest. 

1  Equilibrium,  equal  balance. 


PRESSURE   IN  FLUIDS.  45 

§  44.  Pressure  in  fluids.  —  It  will  be  seen  that,  with  the 
exception  of  the  phenomena  of  capillarity  and  those  occasioned 
by  difference  in  compressibility  and  expansibility,  liquids  and 
gases  are  governed  by  the  same  laws.  We  shall,  therefore,  treat 
them  together,  in  so  far  as  they  are  alike,  under  the  common  term 
of  fluid. 

It  should  be  borne  in  mind  that  we  are  placed  on  the  borders 
of  two  oceans.  A  watery  ocean  borders  our  land ;  an  aerial 
ocean,  which  is  called  the  atmosphere,  surrounds  us.  Every 
molecule,  in  both  the  gaseous  and  liquid  oceans,  is  drawn  to- 
ward the  earth's  centre  by  gravity.  This  gives  to  both  fluids 
a  downward  pressure  upon  everything  upon  which  they  rest. 

The  gravitating  power  of  liquids  is  everywhere  apparent,  as 
in  the  fall  of  drops  of  rain,  the  descent  of  mountain  streams, 
the  power  of  falling  water  to  propel  machinery,  and  the  weight 
of  water  in  a  bucket.  But  to  prove  the  downward  pressure  of 
air  requires  special  experiments.  If  we  lower  a  pail  into  a 
well,  it  fills  with  water,  but  we  do  not  perceive  that  it  becomes 
heavier  thereb}r ;  the  downward  pressure  is  not  felt.  But  when 
we  raise  a  pailful  out  of  the  water,  it  suddenly  becomes  heavy. 
If  we  could  raise  a  pailful  of  air  out  Fig  ^ 

of  the  ocean  of  air,  might  not  the 
weight  of  the  air  become  perceptible  ? 
If  we  dive  to  the  bottom  of  a  pond 
of  water,  we  do  not  feel  the  weight 
of  the  pond  resting  upon  us.  We  do 
not  feel  the  weight  of  the  atmospheric 
ocean  resting  upon  us  ;  but  we  should 
remember  that  our  situation  with  ref- 
erence to  the  air  is  like  that  of  a 
diver  with  reference  to  water. 

Experiment  1.  Fill  two  glass  jars  (Fig.  22)  with  water,  A  having  a 
glass  bottom,  B  a  bottom  provided  by  tying  a  piece  of  sheet-rubber 
tightly  over  the  rim.  Invert  both  in  a  larger  vessel  of  water,  C. 
The  water  in  A  does  not  feel  the  downward  pressure  of  the  air  directly 


46  DYNAMICS. 

above  it,  the  pressure  being  sustained  by  the  rigid  glass  bottom.  But 
it  indirectly  feels  the  pressure  of  the  air  on  the  surface  of  the  water  in 
the  open  vessel,  and  it  is  this  pressure  that  sustains  the  water  in  the 
jar.  But  the  rubber  bottom  of  the  jar  B  yields  somewhat  to  the 
downward  pressure  of  the  air,  and  is  forced  inward,  until  it  is  bal- 
anced by  the  upward  pressure  of  the  water,  plus  the  tension  of  the 
rubber. 

Take  a  glass  tube  D,  lm  long,  having  a  bore  of  lcm  diameter.  Cov- 
ering one  end  with  a  finger,  fill  with  water,  and  invert  in  C.  You  feel 
the  weight  of  the  air  pressing  your  finger  against  the  tube.  Remove 
the  finger  and  the  water  in  the  tube  at  once  sinks  to  the  level  of  the 
water  in  the  vessel  C,  because  the  downward  pressure  of  the  air  on  the 
column  of  water,  plus  the  weight  of  the  column  of  water,  is  greater 
than  the  upward  pressure.  In  every  instance  we  find  that  the  down- 
ward pressure  of  air  gives  rise  to  an  upward  pressure  in  the  liquid.  In 
this  respect  fluids  differ  widely  from  solids,  whose  molecules  are  so 
firmly  held  together  that,  when  one  part  is  pushed  in  any  direction, 
that  part  drags  the  rest  with  it. 

We  have  accounted  for  water  being  sustained  in  the  vessels  A,  B, 

and  D,  by  an  upward  pressure  produced  by  the  downward  pressure  of 

the  air.    Does  this  downward  pressure  create  an  upward  pressure  in 

the  air  itself,  so  that,  if  the  vessels  are  lifted  out  of  the  water,  the 

Fig.  23.  water  will  not  fall  out? 

Experiment  2.  Keeping  the  finger  pressed  on  the 
end  of  D,  raise  it  ,slowly  and  vertically  out  of  the 
water.  The  water  does  not  fall  out.  Why?  Slip 
a  thin  glass  plate,  or  a  piece  of  thick  pasteboard, 
under  the  mouth  of  A,  and,  pressing  it  against  the 
mouth,  raise  the  vessel  carefully  out  of  the  water, 
and  remove  the  hand  from  the  plate.  The  water 
does  not  fall  out,  nor  does  the  plate  fall.  Why? 

Experiment  3.  Force  a  tin  pail  (Fig.  23),  having 
a  hole  in  its  bottom,  as  far  as  possible  into  water, 
without  allowing  water  to  enter  at  the  top.  A  stream  of  water  spurts 
through  the  hole.  Why?  Why  does  it  require  so  much  effort  to 
force  the  pail  down  into  the  water?  Does  downward  pressure  cause 
a  lateral  pressure? 

Experiment  4.  Make  holes,  at  different  depths,  in  the  side  of  a  ves- 
sel (Fig.  24)  containing  water.  Water  issues  in  streams,  with  consid- 
erable force,  from  the  orifices.  Why? 

Experiment  5.    Bind  a  piece  of  thin  sheet-rubber  tightly  over  a 


PRESSURE  INCREASES   WITH  THE  DEPTH. 


47 


Fig.  24. 


wide-mouthed  bottle,  and  place  it  in  water  in  different  positions.  In 
whatever  position  the 
bottle  is  placed,  the  rub- 
ber is  pressed  inward. 
What  lesson  does  this 
teach? 

Experiment  6.     The 
Magdeburg   hemispheres 
(Fig.  25)  are  two  hemis- 
pherical    cups,     having 
their  edges  made  smooth 
so  as  to  be  "air-tight" 
when  placed  in  contact. 
Each  cup  is  provided  with  a  handle.     One  of  the  handles  consists  of 
two  parts,  a  stem  and  a  ring,  the  two  parts  being  connected  by  a  screw. 
The  stem  has  a  bore  passing  through  it,  and  a  stop-cock,        F.    ^ 
which  regulates  the  passage  of  air  through  the  bore. 
Place  the  lips  of  the  cups  in  contact,  remove  the  ring, 
screw  the  stem  to  the  plate  of  an  air-pump,  and  exhaust 
the  air  from  the  sphere ;  then  close  the  stop-cock,  and 
replace  the  ring.     Now  two  boys  grasping  the  rings,  and 
holding  the  sphere  in  any  position  they  choose,  can  only 
with  great  difficulty  pull  them  apart.    Why? 

Boys  amuse  themselves  by  lifting  bricks  (Fig.  26)  with 
a  circular  piece  of  leather,  moistened  and 
pressed  against  the  surface  of  the  brick,  so  as 
to  exclude  the  air.  The  pressure  of  air  against 
the  leather  binds  it  to  the  brick  in  whatever 
position  placed. 

We  conclude  that  gravity  causes  pressure  in  a  body 
of  fluid  in  all  directions. 


Fig.  26. 


§  45.  Pressure  increases  with  the  depth.  —  In  the  ex- 
periment with  the  vessel  with  apertures  in  its  side  (Fig.  24) , 
we  find  that  the  deeper  the  orifice,  the  greater  the  velocity  of 
the  stream.  And  in  the  experiment  with  the  wide- mouthed 
bottle  covered  with  rubber,  we  find  that,  at  the  same  depth,  the 
rubber  is  pressed  inward  equally  in  all  directions,  but,  as  it  is 
carried  to  greater  depths,  the  pressure  is  increased. 


48 


DYNAMICS. 


Fig.  27. 


Fig.  28. 


Experiment.  Take  a  glass  tube  bent  in  the  form  represented  by  a, 
Figure  27 ;  place  mercury  in  the  lower  part  of  the  tube,  so  as  to  fill  the 
short  arm,  and  gradually  lower  the  tube  into  a 
deep  vessel  of  water.  The  downward  pressure 
of  the  water  will  force  the  mercury  up  the  long 
arm  to  a  hight  proportional  to  the  depth  of  the 
tube  in  the  water. 

§  46.  Pressure  at  any  point  in  a  fluid 
equal  in  all  directions.  —  Experiment  1.  In- 
troduce another  tube,  containing  mercury,  of  the 
form  represented  by  b,  Figure  27 ;  lower  both  tubes 
so  that  the  orifices  in  the  water  shall  be  at  the 
same  level,  and  it  will  be  found  that  the  downward 
pressure  in  a  and  the  lateral  pressure  in  b  will  force  the  mercury  to  the 
same  level,  cd. 

Experiment  2.  Cover  one  end  of  a  lamp-chimney  (Fig.  28)  with  a 
circular  piece  of  leather,  and  suspend  from  the  hand  by 
means  of  a  string  attached  to  the  center  of  the  leather 
and  passing  through  the  chimney.  Hold  the  leather 
firmly  against  the  bottom  of  the  chimney,  and  lower  the 
covered  end  a  little  way  into  a  vessel  of  water.  You 
may  now  drop  the  string,  and  the  upward  pressure  of 
the  water  will  keep  the  leather  in  place.  Pour  water 
slowly  into  the  chimney,  and,  when  the  water  in  the 
chimney  nearly  reaches  the  level  of  the  water  outside, 
the  leather  will  fall.  The  upward  pressure  of  the  water 
in  the  vessel  against  the  leather  is  just  balanced  by  the 
downward  pressure  of  the  water  in  the  chimney  and  the 
weight  of  the  leather.  Why  does  not  a  pailful  of  water  in  a  well  seem 
heavy  ? 

The  results  of  experiments  thus  far  show  that,  at  every  point 
in  a  body  of  fluid,  gravity  causes  pressure  to  be  exerted  equally  in 
all  directions,  and  that  in  liquids  the  pressure  increases  as  the 
depth  increases. 

Have  we  any  means  of  ascertaining  the  pressure  at  any  point 
in  the  atmosphere  ? 

Experiment  3.  Prepare  a  U-shaped  glass  tube  closed  at  one  end 
(Fig.  29),  80cm  in  hight  from  the  center  of  the  bend,  and  with  a  bore  of 
iqcm  section.  Fill  the  closed  arm  with  mercury  and  invert.  The  mer- 


PRESSURE  AT   ANY  POINT   IN  A  FLUID.  49 

cury  in  the  closed  arm  will  sink  about  2cm  to  A,  and  will  rise  2cm  in  the 
open  arm  to  C ;  but  the  surface  A  is  76cm  higher  than  the  surface  C. 
This  can  be  accounted  for  only  by  the  atmos-  .— 

pheric  pressure.  The  column  of  mercury' B  A, 
containing  76ccm,  is  an  exact  counterpoise  for  a 
column  of  air  of  the  same  diameter  extending 
from  C  to  the  upper  limit  of  the  atmospheric 
ocean,  —  an  unknown  hight. 

The  weight  of  the  76ccm  of  mercury  in  the 

column  BA   is   1033. 3*  exactly,  but,   for 

convenience,  may  be  said  to  be  about  lk. 

Hence  the  weight  of  a  column  of  air  of 

lqcm  section,  extending  from  the  surface  of 

tbe  sea  to  the  upper  limit  of  the  atmosphere, 
Fig.  so.  is  about  lk.   But 

gravity  causes 
equal  pressure 
in  all  directions. 
Hence,  at  the 
level  of  the  sea, 

all  bodies  are  pressed  upon  in  all 
directions  by  the  atmosphere,  with  a 
force  of  about  lk  per  square  centi- 
meter, about  15  pounds  (exactly  14. 7 
Ibs.)  per  square  inch,  or  about  one 
ton  per  square  foot.  Fluid  pressure 
is  generally  expressed  in  atmos- 
pheres. An  atmosphere  (when  the 
term  is  used  to  denote  pressure)  is 
the  pressure  of  P  per  square  centi- 
meter. 

A  man  of  average  size  sustains  an  ex- 
ternal pressure  of  about  fifteen  tons.  If  the  area  of  the  bottom  of  an 
"  empty  "  pail  is  one  square  foot,  the  downward  pressure  on  its  bottom 
is  a  little  more  than  one  ton ;  how  can  any  person  carry  such  a  pail? 
and  why  is  its  bottom  not  forced  out? 


50 


DYNAMICS. 


§  47.   Barometer.  —  Figure  30  represents  another  form  of  ap- 
paratus, which  is  more  commonly  used  for  ascertaining  atmospheric 
pressure.    It  Consists  of  a  straight  tube  about  85cm  long,  closed  at 
one  end,  and  filled  with  mercury.    When  this  tube  is  inverted,  the 
Fig  3]  open    end    having 

been  covered  wHh  a 
finger  and  plunged 
into  an  open  cup  of 
mercury,  and  the 
finger  withdrawn, 
the  mercury  in  the 
tube  will  sink  till 
it  balances  the  at- 
mospheric press- 
ure. This  experi- 
ment was  devised 
by  Torricelli,  an 
Italian.  The  ap- 
paratus is  called  a 
barometer.1  The 
empty  space  above 
the  mercury  in  the 
tube  is  called  a  Tor- 
ricellian vacuum. 
The  history  of  this 
experiment  is  very 
interesting  and  im< 
portant,  inasmuch 
as  it  was  the  first 
demonstration  of 
the  pressure  of  the 
atmosphere.  (See 
Whewell's  History  of  Inductive  Sciences,  Vol.  I.,  page  345.) 
The  hight  of  the  barometric  column  is  subject  to  fluctuations ; 

1  Barometer,  weight  measurer. 


BAROMETER.  51 

this  shows  that  the  atmospheric  pressure  is  subject  to  variations 
from  various  causes.  The  barometer  is  always  a  faithful  moni- 
tor of  all  changes  in  atmospheric  pressure.  It  is  also  service- 
able as  a  weather  indicator.  Not  that  any  particular  point  at 
which  mercury  may  stand  foretells  any  particular  kind  of 
weather,  but  any  sudden  change  in  the  barometer  indicates  a 
change  in  the  weather.  A  rapid  fall  of  mercury  generally  fore- 
bodes a  storm,  while  a  rising  column  indicates  clearing  weather. 

If  the  barometer  is  carried  up  a  mountain,  it  is  found  that  the 
mercury  constantly  falls  as  the  ascent  increases.  This  shows 
that  the  pressure  is  greater  near  the  bottom  of  the  aerial  *>cean 
than  near  its  top.  It  is  found  that  the  pressure  increases  very 
rapidly  near  the  bottom,  as  may  be  understood  by  studying 
Figure  31.  The  shading  shows  the  variation  in  density  of  the 
air.  The  figures  in  the  left  margin  show  the  hight  of  the  atmos- 
phere, in  miles ;  those  on  the  right  the  corresponding  hight  of 
the  mercury,  in  inches.  The  average  hight  of  the  mercurial 
column,  at  the  level  of  the  sea,  is  about  76cm  (80  inches). 

It  will  be  seen  that  the  density  at  a  hight  of  3  miles  is  but 
little  more  than  J  the  density  at  the  sea-level ;  at  6  miles,  £ ;  at 
9  miles,  % ;  at  15  miles,  -^ ;  at  35  miles  it  is  calculated  to  be 
only  3-^77,  so  that  the  greatest  part  of  the  atmosphere  must  be 
within  that  distance  of  the  surface  of  the  earth.  On  the  other 
hand,  if  an  opening  could  be  made  in  the  earth,  35  miles  in 
depth  below  the  sea-level,  it  is  calculated  that  the  density  of  the 
air  at  the  bottom  would  be  1,000  times  greater  than  at  the  sea 
level,  so  that  water  would  float  in  it.  Air  has  been  compressed 
to  this  density. 

To  what  hight  the  atmosphere  extends  is  unknown.  It  is 
variously  estimated  at  from  50  to  200  miles.  If  the  aerial  ocean 
were  of  uniform  density,  and  of  the  same  density  that  it  is  at 
the  sea-level,  its  depth  would  be  a  little  short  of  five  miles. 
Certain  peaks  of  the  Himalayas  would  rise  above  it.  It  may  be 
readily  seen  that  hights  of  mountains  may  be  measured  approxi- 
mately by  the  aid  of  a  barometer. 


52  DYNAMICS. 

QUESTIONS. 

1.  A  person  on  the  top  of  Mt.  Blanc  would  take  in  what  portion  of 
the  air,  on  expanding  his  lungs  to  a  certain  extent,  that  he  would  at 
the  bottom  ? 

2.  How  would  this  affect  breathing,  considering  that  a  person  re- 
quires a  definite  amount  of  air  in  a  given  time,  in  order  to  sustain 
life? 

3.  A  person  ascending  6  miles  in  a  balloon  leaves  what  proportiona\ 
part  of  the  whole  mass  of  air  below  him  ? 

4.  When  the  barometric  column  stands  at  492mm,  what  is  the  atmos- 
pheric pressure  in  grams  per  square  centimeter  ? 

5.  A  barometer  carried  into  a  mine  stands  at  982ram ;  what  is  the 
atmospheric  pressure  in  the  mine  ?  , 

U 

§  48.  Compressibility  and  expansibility  of  gases. — The 
increase  of  pressure  attending  the  increase  in  depth,  in  both 
liquids  and  gases,  is  readily  explained  by  the  fact  that  the  lower 
layers  of  fluids  sustain  the  weight  of  all  the  layers  above.  Con< 
sequently,  if  the  body  of  fluid  is  of  uniform  density,  as  is  very 
nearly  the  case  in  liquids,  the  pressure  will  increase  in  nearly 
the  same  ratio  as  the  depth  increases.  But  the  aerial  ocean  is 
far  from  being  of  uniform  density,  in  consequence  of  the  extreme 
compressibility  of  gaseous  matter.  The  contrast  between  water 
and  air,  in  this  respect,  may  be  seen  in  the  fact  that  water,  sub- 
jected to  a  pressure  of  one  atmosphere,  contracts  .0000457  of 
its  volume ;  under  the  same  circumstances,  air  contracts  one- 
half.  For  most  practical  purposes,  we  may  regard  the  density 
of  water  at  all  depths  as  uniform,  while  it  is  far  otherwise  in 
large  masses  of  gases. 

The  pressure  at  different  depths  in  liquids  may  be  illustrated 
by  piling  several  bricks  one  on  another,  when  the  pressures  that 
different  bricks  sustain  vary  directly  with  their  depths  below 
the  upper  surface  of  the  pile.  On  the  other  hand,  pressure  of 
gases  at  different  depths  may  be  illustrated  by  piling  fleeces  of 
wool  one  on  another.  Since  the  volume  of  each  successive 
fleece  varies  with  the  weight  it  bears,  the  pressures  which  differ- 
ent fleeces  sustain  are  not  proportional  to  their  respective  depths 


COMPKESSIBILITY  AND   EXPANSIBILITY   OF  GASES.    53 

below  the  upper  surface  of  the  pile.  At  twice  the  depth, 
there  would  be  much  more  than  twice  the  pressure,  because 
the  lower  point  would  sustain  more  than  twice  the  number  of 
fleeces. 

Closely  allied  to  compressibility  is  the  elasticity  of  gases,  or 
their  power  to  recover  their  former  volume  after  compression. 
The  elasticity  of  all  fluids  is  perfect.  By  this  is  meant,  that  the 
force  exerted  in  expansion  is  always  equal  to  the  force  used  in 
compression ;  and  that,  however  much  a  fluid  is  compressed,  it 
will  always  completely  regain  its  former  bulk  when  the  pressure 
is  removed.  Liquids  are  perfectly  elastic ;  but,  inasmuch  as 
they  are  perceptibly  compressed  only  under  tremendous  pres- 
sure, they  are  regarded  as  practically  incompressible,  and  so  it  is 
rarely  necessary  to  consider  their  elasticity.  It  has  alread}7  been 
stated  (page  17)  that  matter  in  a  gaseous  state  expands  indefi- 
nitely, unless  restrained  by  external  force.  The  atmosphere  is 
confined  to  the  earth  by  the  force  of  gravit}'. 

Experiment.  Partially  fill  an   india-rubber  balloon  with  air,  and 
tightly  close  it.     What  is  the  external  force  that  prevents  the  air  in  the 
balloon  from  expanding  and  completely  in- 
flating the  balloon  ?    Place  it  under  the  glass 
receiver  of  an  air-pump  (Fig.  32),   and  ex- 
haust the  air;    the  balloon    becomes    com- 
pletely distended,  and  possibly  bursts.   Before 
it  is  placed  under  the  receiver,  the  balloon 
Fig  33  sustains  a  pressure   of  15 

pounds  on  every  square 
inch.  What  prevents  a  col- 
lapse under  this  pressure  ? 
Inasmuch  as  the  balloon 
shows  no  signs  of  disten- 
tion,  or  collapse,  until 

placed  under  the  receiver,  it  would  seem  that  this 
great  outward  pressure  is  exactly  balanced  by  the 
tension  of  the  air  within. 

Glass-blowers  prepare  thin  glass  bottles  (Fig.  33) 
for  the  purpose  of  illustrating  the  tension  of  air.  Containing  air  of 
ordinary  density,  they  are  sealed  and  placed  under  the  receiver  of  an 


54 


DYNAMICS. 


Fig.  34. 


air-pump;  the  surrounding  air  (in  other  words,  +he  outside  pressure)  is 
removed,  and  the  enclosed  air  then  bursts  the  bottles,  throwing  frag- 
ments of  glass  in  all  directions. 

At  every  point,  then,  in  a  body  of  air,  forces  are  acting  out- 
wards. The  air  is  somewhat  like  a  spring  coiled  up,  and  ready 
to  relax  itself,  when  opportunity  is  given.  Since  this  elastic 
force  at  the  bottom  of  the  column  exactly  balances  the  force  o.' 
gravity  acting  on  the  whole  column,  i.e.,  equals  the  weight  of  the 
whole'  column,  it  follows  that,  at  the  sea-level,  the  elastic  force 
of  air  is  ordinarily  lk  per  square  centimeter. 

§  49.  Air-pump.  —  The  air-pump,  as  its  name  implies,  is 
used  to  withdraw  air  from  a  closed  vessel.  Figure  34  will  serve 

to  illustrate  its  oper- 
ation. R  is  a  glass 
receiver  from  which 
air  is  to  be  exhausted . 
B  is  a  hollow  cylin- 
der of  brass,  called 
the  pump-barrel.  A 
plug  P,  called  a  pis- 
ton, is  fitted  to  the 
interior  of  the  barrel, 
and  can  be  moved 
up  and  down  by  the 
handle  H ;  s  and  t 
are  valves.  A  valve 
acts  on  the  principle 

of  a  door  intended  to  open  or  close  a  passage.  If  you  walk 
against  a  door  on  one  side,  it  opens  and  allows  you  to  pass  ;  but 
if  you  walk  against  it  on  the  other  side,  it  closes  the  passage, 
and  stops  your  progress.  Suppose  the  piston  to  be  in  the  act 
of  descending.  The  compression  of  the  air  in  B  closes  the  valve 
£,  and  opens  the  valve  s,  and  the  enclosed  air  escapes.  After 
the  piston  reaches  the  bottom  of  the  barrel,  it  begins  its  ascent ; 
when  the  air  above  the  piston,  in  attempting  to  rush  down 


THE  AIR-PUMP.  55 

to  fill  the  vacuum  that  is  formed  between  the  bottom  of  the 
barrel  and  the  piston,  closes  the  valve  s.  But  as  soon  as  a 
vacuum  is  formed  above  £,  and  the  downward  pressure  on  the 
valve  removed,  the  air  in  R  expands,  opens  the  valve  £,  and  fills 
the  space  in  B  that  would  otherwise  be  a  vacuum.  But,  as  the 
air  in  R  expands,  it  becomes  rarefied  ;  and,  as  there  is  less  air, 
so  there  is  less  tension.  The  external  pressure  of  the  air  on  R, 
being  no  longer  balanced  by  the  tension  of  the  air  within,  presses 
the  receiver  firmly  upon  the  plate  L.  Each  repetition  of  a 
double  stroke  of  the  piston  removes  a  portion  of  the  air  remain- 
ing in  R.  The  air  is  removed  from  R  by  its  own  expansion. 
However  far  the  process  of  exhaustion  may  be  carried,  the 
receiver  will  always  be  filled  with  air,  although  it  may  be  exceed- 
ingly rarefied.  The  operation  of  exhaustion  is  practically  ended 
when  the  tension  of  the  air  in  R  becomes  too  feeble  to  lift  the 
valve  t. 

D  is  another  receiver,  opening  into  the  tube  T,  that  connects 
the  receiver  with  the  barrel.  Inside  the  receiver  is  placed  a 
barometer.  It  is  apparent  that  air  is  exhausted  from  D  as  well 
as  from  R ;  and,  as  the  pressure  is  removed  from  the  surface  of 
the  mercury  in  the  cup,  the  barometric  column  falls ;  so  that 
the  barometer  serves  as  a  gauge  to  indicate  the  approximation 
to  a  vacuum.  For  instance,  when  the  mercury  has  fallen  380mm 
(15  inches),  one-half  of  the  air  has  been  removed. 

QUESTIONS. 

1.  Why  is  it  difficult  for  a  person  to  lift  the  receiver  from  the  pump 
after  the  air  is  exhausted  from  it  ? 

2.  Why  is  it  easily  raised  before  the  air  is  exhausted  ? 

3.  Suppose  that  the  air  in  the  pump-barrel,  when  the  piston  is  raised, 
is  one-eighth  of  all  the  air  in  the  pump,  including  the  air  in  the  receiv- 
ers ;  what  portion  of  the  air  is  removed  by  the  first  double  stroke  ? 

4.  What  portion  of  the  original  amount  of  air  is  removed  at  the 
second  double  stroke? 

5.  Which  double  stroke  removes  the  most  air  ? 

6.  If  there  were  no  force  required  to  lift  the  valve  t,  why  could  not 
a  perfect  vacuum  be  obtained  ? 


56 


DYNAMICS. 


Fig.  35. 


7.  It  is  a  very  good  pump  that  reduces  the  hight  of  the  mercurial 
column  to  3mm.  What  portion  of  the  air  has  been  removed  in  that 
case  ? 

An  absolute  vacuum  nas  never  been  attained.  The  difficulty 
may  be  readily  understood.  According  to  the  most  recent  cal- 
culations, the  number  of  molecules 
contained  in  a  cubic  centimeter 
of  air  of  ordinary  density  is  some- 
thing like  21,000,000,000,000,- 
000,000  (twenty-one  million  tril- 
lion) ;  consequently,  when  it  is 
reduced  to  one-millionth  its  us- 
ual density,  21,000,000,000,000 
(twenty-one  trillion)  molecules 
are  still  left.  The  exhaustion 
may  be  carried  much  farther  than 
by  purety  mechanical  means,  by 
heating  a  piece  of  charcoal  in 
the  receiver  while  the  pumping  is 
going  on.  Heat  expels  the  air 
in  its  pores.  After  the  pumping 
has  ceased,  the  charcoal  is  al- 
lowed to  cool,  when  it  condenses 
a  large  portion  of  the  remaining 
air  in  its  pores.  (See  §  37,  page 
38.) 

A  very  cheap  and  efficient  sub- 
stitute for  an  air-pump  for  many  purposes  may  be  arranged  as 
in  Figure  35,  in  which  a  is  an  elevated  tank  of  water  having  a 
faucet  b  by  which  the  rapidity  of  the  flow  of  water  may  be  regu- 
lated. The  tube  c  should  be  as  long  as  the  hight  of  the  room 
will  admit,  and  its  lower  end  should  dip  into  a  cup  of  water  d. 
To  the  end  of  the  branch-pipe  e  there  may  be  connected,  by 
means  of  rubber  tubing  ft,  a  glass  tube  leading  to  a  vessel  #,  from 
which  air  is  to  be  exhausted.  Water  falling  freely  through  a 


MAKIOTTE'S  LAW. 


57 


vertical  tube  exerts  no  lateral  pressure ;  consequently  there  is 
no  tendency  to  enter  the  branch  e.  As  the  water  in  falling 
increases  in  velocity,  it  tends  to  separate,  leaving  between  the 
cylinders  of  water  vacuous  spaces.  The  lower  end  of  the  pipe  c 
being  immersed  in  water,  air  cannot  enter  there  ;  Fig  36 

but  the  air  in  the  receiver  g  expands  and  rushes 
through  the  tube  e,  to  fill  these  vacua,  and  thus 
exhaustion  is  effected.  In  SprengePs  air-pump 
mercury  is  substituted  for  water,  and  air  is  reduced 
by  it  to  less  than  one-millionth  its  usual  density. 

Experiment  1.  Take  a  glass  tube  (Fig.  36) ,  having 
a  bulb  blown  at  one  end.  Nearly  fill  it  with  water,  so 
that  when  inverted  there  will  be  only  a  bubble  of  air  in 
the  bulb.  Insert  the  open  end  in  a  glass  of  water,  place  under  a 
receiver,  and  exhaust.  Nearly  all  the  water  will  leave  the  bulb  and 
tube.  Why?  What  will  happen  when  air  is  admitted  to  the  receiver? 

Experiment  2.  Through  a  cork  of  a  tightly-stopped  bottle  pass  one 
arm  of  a  U-shaped  glass  tube  C  (Fig.  37). 
Introduce  the  other  arm  into  the  empty  Fi&-  37- 

vessel  B.  Place  the  whole  under  a  glass 
receiver,  and  exhaust  the  air.  What  phe- 
nomena will  occur?  What  will  happen 
when  air  is  admitted  to  the  receiver? 


§  50.  Maftotte's  Law.  —  The 
experiment  illustrated  by  Figure  32 
showed  that  the  volume  of  a  given 
body  of  gas  depends  upon  the  pres- 
sure to  which  it  is  subjected.  To 
find  more  exactly  the  relation  between  these  quantities,  proceed 
as  follows :  — 


Experiment  1.  Take  a  bent  glass  tube  (Fig.  38),  the  short  arm 
being  closed,  and  the  long  arm,  which  should  be  at  least  85cm  long, 
being  open  at  the  top.  Pour  mercury  into  the  tube  till  the  surfaces  in 
the  two  arms  stand  at  zero.  Now  the  surface  in  the  long  arm  supports 
the  weight  of  an  atmosphere.  Therefore  the  tension  of  the  air  en- 


58 


DYNAMICS. 


Fig.  38. 


closed  in  the  short  arm,  which  exactly  balances  it,  must  be  about  15 
pounds  to  the  square  inch.  Next  pour  mercury  into  the  long  arm  till  the 
surface  in  the  short  arm  reaches  5,  or  till  the  volume  of  air  enclosed  is 
reduced  one-half,  when  it  will  be  found  that  the  hight  of  the  column  A  C 
is  just  equal  to  the  hight  of  the  barometric  column 
at  the  time  the  experiment  is  performed.  It  now 
appears  that  the  tension  of  the  air  in  A  B  balances 
the  atmospheric  pressure, plus  a  column  of  mercury 
A  C,  which  is  equal  to  another  atmosphere ;  .*.  the 
tension  of  the  air  in  A  B  =  two  atmospheres.  But 
the  air  has  been  compressed  into  half  the  space  it 
formerly  occupied,  and  is,  consequently,  twice  as 
dense.  If  the  length  and  strength  of  the  tube 
would  admit  of  a  column  of  mercury  above  the 
surface  in  the  short  arm  equal  to  twice  A  C,  the 
air  would  be  compressed  into 
one-third  its  original  bulk;  and, 
inasmuch  as  it  would  balance  a 
pressure  of  three  atmospheres,  its 
tension  would  be  increased  three- 
fold. 

Experiment  2.  Next  take  a 
glass  tube  (Fig.  39)  open  at  both 
ends,  and  about  24  inches  long. 
Tie  three  strings  around  the  tube, 
—  one  3  inches  from  the  top, 
another  6  inches,  and  the  third  21 
inches.  Nearly  fill  a  glass  jar,  B, 
25  inches  high  with  mercury. 
Lower  the  tube  into  the  mercury 
till  it  reaches  the  string  at  3. 
Press  a  finger  firmly  over  the  up- 
per end,  and  raise  the  tube  till  the 
string  at  21  is  on  a  level  with  the  surface  of  the  mer- 
cury in  the  jar.  The  mercury  in  the  tube  will  stand  at 
6.  At  first  the  air  enclosed  in  the  tube  between  3  and 
the  finger  withstands  an  upward  pressure  of  the  mer- 
cury sufficient  to  sustain  a  column  of  mercury  30  inches  high,  or  one 
atmosphere.  When  the  tube  is  raised  and  the  mercury  stands  at  6,  15 
inches  high,  one-half  of  that  upward  pressure  is  exerted  in  sustaining 
the  15  inches  of  mercury,  and  the  other  half  is  exerted  on  the  enclosed 


QUESTIONS. 


59 


air.  But  the  pressure  on  the  air  is  reduced  one-half,  while  the  volume 
is  doubled.  The  results  of  the  two  sets  of  experiments  may  be  tabu- 
lated as  follows :  — 


Pressure   . 
Volume     . 
Density     .     , 
Elastic  force 


i,  J,  1,  2,  3,  4,  &c. 

3,  2,  1,  J,  J,  i,  &c. 

J,  },  1,  2,  3,  4,  &c. 

J,  i,  1,  2,  3,  4,  &c. 


From  these  results  we  learn  that,  at  twice  the  pressure  there 
is  half  the  volume,  while  the  density  and  elastic  force  are 
doubled.  At  half  the  pressure  the  volume  is  doubled,  and 
the  density  and  elastic  force  are  reduced  one-half.  Hence  the 
law :  The  volume  of  a  body  of  gas  varies  inversely  as  the  pres- 
sure^ density,  or  elastic  force.  This  is  sometimes  called  Mariotte's, 
and  sometimes  Boyle's,  law,  from  the  names  of  the  two  men 
who  discovered  it  at  about  the  same  time.  This  law  is  true  for 
all  gases  within  certain  limits,  but  under  extreme  pressure  the 
reduction  in  volume  is  greater  than  indicated  by  it.  The  greatest 
deviation  from  it  occurs  with  those  gases  that  are  most  easily 
liquefied. 

QUESTIONS. 

1.  Into  the  neck  of  a  bottle  partly  filled  with  water  (Fig.  40),  in- 
sert a  cork  very  tightly,  through  which  passes  a  glass 
tube  nearly  to  the  bottom  of  the  bottle.  Blow  forci- 
bly into  the  bottle.  On  removing  the  mouth,  water 
will  flow  through  the  tube  in  a  stream.  Why? 

2.  How  can  an  ounce  of  air, 
in  a  closed  fragile  vessel,  sus- 
tain the  outside  pressure  of 
the  atmosphere,  amounting  to 
several  tons?     . 

3.  What  drives  the  pellets 
from  a  pop-gun  ? 

4.  Figure  41  represents   a 
dropping-bottle,  much  used  in 
chemical  laboratories.      Why 
do  bubbles  of  air  force  their 
way  down  into  the  liquid? 

5.  Stop  the  upper  orifice,  and  the  liquid  will  quickly  cease  to  drop. 
Why? 


Tig.  40. 


Fig.  41. 


60  DYNAMICS. 

6.   The  inconvenience  arising,  in  many  culinary  and  laboratory  oper- 
ations, from  water  "  boiling  away,"  may  be  remedied  as  represented  in 
Figure  42.     A  bottle  filled  with  water  is  so  suspended  that  its  mouth 
Fig  42  is  Just  below  ^e  surface  of  the  boiling  liquid.     As 

the  water  evaporates,  and  its  surface  falls  below  the 
mouth  of  the  bottle,  an  air-bubble  enters  the  bottle, 
expands,  and  pushes  out  enough  water  to  cover  once 
more  the  mouth  of  the  bottle.  Why  does  not  the  air 
push  out  all  the  water  from  the  bottle? 

7.  Figure  43  represents  a  weight-lifter.     Into  a 
hollow  cylinder  s  is  fitted  air-tight  a  piston  t.    The 
cylinder  is  connected  with  an  air-pump  by  a  rubber 
tube  u.    When  air  is  exhausted  the  piston  rises,  lift- 
ing the  heavy  weight  attached  to  it.    Why? 

8.  If  the  area  of  the  lower  surface  of  the  piston  is 
20<icm,  how  heavy  a  weight  ought  to  be  lifted  when 
the  air  is  one-half  exhausted  ? 

9.  Suppose  you  tightly  stopper  a  bottle  at  the  top  of  Mont  Blanc,  car- 
ry it  to  the  sea-level, 
insert  the  mouth  of 
the  bottle  in  water, 
and  withdraw  the 
stopper ;  what  would 
happen  ? 

10.  Show  that  the 
labor  of  working  the 
kind  of  air-pump  de- 
scribed (§49)  increas- 
es as  the  exhaustion 
progresses. 

§51.  Condenser. 
—  In  the  experi- 
ment with  the  bottle 
(Fig.  40),  air  was 
condensed  in  the 
mouth  by  muscular 
contraction,  and  forced  into  the  bottle.  An  apparatus  A  (Fig. 
44),  intended  to  condense  air  in  a  closed  vessel,  is  called  a 
condenser.  Its  construction  is  like  that  of  the  barrel  of  the 


PRESSURE  TRANSMITTED  UNDIMINISHED,   ETC.        61 


air-pump,  except  that  the  position  of  the  valves  is  reversed. 
(Compare  with  Fig.  34.)  What  differences  do  you  notice  in 
respect  to  the  valves?  What  happens  to 
the  valves  when  the  piston  in  the  condenser 
is  forced  down?  If  the  condenser  is  con- 
nected with  a  closed  vessel  B,  how  much 
air  would  be  forced  into  it  at  one  down 
stroke?  What  prevents  the  air  from  es- 
caping during  an  up  stroke?  If,  after  air  is 
condensed  in  B,  the  cylinder  C  is  connected 
with  it  by  a  screw,  and  the  stop-cock  t  is 
suddenly  turned,  what  would  happen  to  the 
bullet  s  ?  What  name  would  you  give  to  such 
an  apparatus? 

The   Western  Union  Telegraph  Company,  in 
New  York  City,  employs  atmospheric  pressure  in 
forwarding  messages  to  its  central  office  from 
the  various  telegraph  stations  in  that  city.    Tubes  of  uniform  size,  free 
from  sudden  curvatures,  and  laid  under  ground,  connect  the  branch 

8        offices  with  headquarters.    Rolls  of  paper,  or  letters  to  be  des- 
c     patched,  are  deposited  in  a  cylindrical  box  c  (Fig.  45),  which 
fits  the  interior  of  the  tube.    The  box  being  dropped  into  the 
h   *  end  of  the  tube 

d  o  g-K 

Fig.  45.  at  a,  and  the  air 

being  exhausted 
from  the  tube  at 
the  end  6,  by 
means  of  an  air- 
pump  worked  by 
steam,  air  rushes 
in  at  a  and  pushes 

the  box  through  the  tube  with  a  force  of  several  pounds  for  every  square 
inch  of  the  end  of  the  box.  The  operation  is  still  further  facilitated 
by  the  aid  of  a  condensing-pump  worked  by  steam  at  the  end  a. 

§  52.  Pressure  transmitted  undiminished  in  all  direc- 
tions. —  Fill  the  globe  G  (Fig.  46) ,  and  about  one-fifth  the  cylin- 
der C,  with  water.  The  water  in  the  tubes  a,  6,  c,  and  d,  will  rise 


DYNAMICS. 


Fig.  46. 


to  the  same  level  with  the  water  in  the  cylinder  C.  Now  force 
the  piston  P  into  the  cylinder,  and  the  downward  pressure  will 
cause  jets  of  water  to  issue  from  each  of  the  tubes.  But  the 
streams  from  the  tubes  a,  6,  and  c,  rise  to  exactly  the  same 
hight  that  the  stream  from  the  tube  d  does,  although  the  liquid 

in  the  latter  tube  re- 
ceives the  direct  ac- 
tion of  the  downward 
force.  It  thus  appears 
that  the  pressure  is  not 
felt  alone  by  that  por- 
tion of  the  liquid  that 
lies  in  the  path  of  the 
force,  but  is  felt  equally 
in  all  parts  and  in  all 
directions. 

If  the  globe  is  filled 
with  air,  and  subjected 
to  pressure  as  above, 
currents  of  air  will  is- 
sue from  the  several 
tubes  with  equal  force. 
This  property  of  trans- 
mitting pressure  equal- 
ly in  all  directions, 
which  is  peculiar  to  fluids,  is  due  to  their  mobility  and  perfect 
elasticity. 

Figure  47  represents  a  number  of  elastic  hoops  enclosed  in 
the  vessel  ABCD.  A  weight,  placed  on  a,  communicates  to 
it  a  downward  pressure.  It  is  evident,  that  not  only  is  the 
pressure  communicated  to  the  hoops  below  it  in  succession,  and 
finally  to  the  bottom  of  the  box,  but  there  is  also  a  lateral  pres- 
sure due  to  the  elastic  property  of  the  hoops.  The  hoop  c, 
receiving  pressure  from  6,  above,  reacts,  exerting  an  upward 
pressure  ;  it  also  presses  laterally  upon  the  side  A,  and  the  hoop 


PRESSURE  TRANSMITTED   UNDIMINISHED,  ETC.         63 


n,  and  downward  upon  d  ;  d  and  n  in  turn  transmit  pressure  to 
their  adjacent  hoops,  and  thus  every  hoop  receives  and  trans- 
mits, upward,  downward,  and 
laterally,  a  force  equal  to  the 
downward  pressure  of  the  weight 
W.  Hence  that  portion  of  the 
bottom  immediately  under  the 
weight  receives  no  greater  pres- 
sure from  W  than  an  equal  area 
of  any  other  part  of  the  bottom, 
or  than  an  equal  area  of  either 
of  the  sides,  A  and  B,  or  the  top 
C.  This  operation  illustrates, 
somewhat  imperfectly,  the  meth- 
od by  which  elastic  fluids  trans- 
mit pressure  undiminished  in  all 
directions. 

If  we  take  a  quantity  of  water 
in  a  vessel  A  (Fig.  48),  shut 
in  by  two  pistons,  a  and  6,  whose  areas  are  respectively 
16qcra  and  4qcm,  and  place  a  10-gram  weight  on  the  platform  d, 
and  an  equal  weight  on  the  platform  c,  it  will  be  found  that 
the  latter  is  not  sufficient  to  balance  the 
former,  but  that  it  will  require  a  40-gram 
weight  placed  on  c  to  preserve  equilibrium. 
But  the  area  of  the  piston  b  is  4qcm,  while 
the  piston  a  contains  four  such  areas ; 
hence  it  follows  that  a  pressure  of  10 g  is 
transmitted  to  each  of  the  4qcm  of  a,  and  just 
supports  the  40-gram  weight.  Had  the  area 
of  the  piston  b  been  lqcm,  then  the  10-gram 
weight  placed  on  it  would  require  a  160-gram 
weight  placed  on  a  to  balance  it;  that  is,  a  pressure  of  10g 
would  be  exerted  on  every  square  centimeter  of  a. 

Obviously  this  form  of  apparatus  cannot  be  made  to  work  well  on 


Fipr.  48. 


64  DYNAMICS. 

• 

account  of  the  friction  of  the  pistons;  but  we  may  substitute  for 
the  pistons  and  weights  columns  of  liquids.  For  instance,  let  the 
connecting  tube  and  the  lower  part  of  the  barrels  be  filled  with  mer- 
cury; the  two  free  surfaces  will  be  at  the  same  level.  Now  if  10s 
of  any  liquid,  e.g.  water,  is  poured  into  b,  the  level  of  the  mercury 
will  be  changed;  and,  to  bring  it  back  to  its  original  level,  40«  of  some 
liquid  must  be  poured  into  a. 

We  conclude,  therefore,  that  a  pressure  exerted  on  a  given 
area  of  a  fluid  enclosed  in  a  vessel  is  transmitted  to  every  equal 
area  of  the  interior  of  the  vessel ;  and  that  the  whole  pressure  that 
may  be  exerted  upon  the  vessel  may  be  increased  in  proportion  as 
the  area  of  the  part  subjected  to  external  pressure  is  decreased. 

§  53.   Hydrostatic  bellows.  —  This  principle  is  well  illus- 
trated by  means  of  the  hydrostatic  bellows.     Two  boards,  b  and 
Fig  49  c  (Fig.  49),  each  having  an  area  of  (say) 

400qcm,  are  so  connected,  by  leather  at- 
tached to  their  edges,  as  to  form  an  air- 
tight vessel  called  the  bellows.  A  glass 
tube  a,  having  a  bore  of  lqcm  section, 
communicates  with  the  interior  of  the  bel- 
lows. Let  water  be  poured  into  the  tube 
a  till  the  board  b  is  raised  a  few  centime- 
ters. The  water  will  stand  at  the  same 
hight  in  the  tube  and  bellows.  Now,  if 
50g  of  water  be  poured  into  the  tube,  it 
will  require  a  weight  of  20,000g  to  be 
placed  upon  b  to  prevent  its  rising.  Any 
weight  less  than  that  will  be  raised  by 
the  50g  of  water.  If,  instead  of  water  being  introduced  into  the 
bellows,  a  person  stand  on  &,  and  blow  into  the  tube,  he  can 
easily  raise  himself  by  the  force  of  his  breath. 

§  54.  Hydrostatic  press.  —  Closely  allied  to  the  bellows  is 
the  hydrostatic  press,  sometimes  called  Bramahs  press  from  the 
name  of  the  inventor.  You  see  two  pistons,  t  and  s,  Figure  50. 


.    . 


PRESSURE  IN  FLUIDS   DUE   TO   GRAVITY, 


65 


The  area  of  the  lower  surface  of  t  is  (say)  one  hundred  times 
that  of  the  lower  surface  of  s.  As  the  piston  s  is  raised  and 
depressed,  water  is  pumped  up  from  the  cistern  A,  forced  into 
the  cylinder  #,  and  exerts 
an  upward  pressure 
against  the  piston  t  one 
hundred  times  greater 
than  the  downward  pres- 
sure exerted  upon  s. 
Thus,  if  a  pressure  of  one 
hundred  pounds  is  applied 
at  s,  the  cotton  bales  will 
be  subjected  to  a  pressure 
of  five  tons. 

The  pressure  that  may 
be  exerted  by  these  press- 
es is  enormous.  The  hand 
of  a  child  can  break  a 
strong  iron  bar.  But  observe  that,  although  the  pressure  ex- 
erted is  very  great,  the  upward  movement  of  the  piston  t  is 
very  slow.  In  order  that  the  piston  t  may  rise  lcm,  the  piston  s 
must  descend  100cm.  The  disadvantage  arising  from  slowness  of 
operation  is  little  thought  of,  however,  when  we  consider  the 
great  advantage  accruing  from  the  fact  that  one  man  can  pro- 
duce as  great  a  pressure  with  the  press  as  a  hundred  men  can 
exert  without  it. 

The  press  is  used  for  compressing  cotton,  hay,  etc.,  into  bales, 
and  for  extracting  oil  from  seeds.  The  modern  engineer  finds 
it  a  most  efficient  machine,  whenever  great  weights  are  to  be 
moved  through  short  distances,  as  in  launching  the  Great  East- 
ern steamship. 

§  55.  Pressure  in  fluids  due  to  gravity.  —  Having  con- 
sidered the  transmission  to  the  walls  of  the  containing  vessel,  of 
external  pressure  applied  to  any  portion  of  a  surface  of  a  liquid, 


66  DYNAMICS. 

we  will  examine  the  effects  of  pressure  due  to  the  weight  of  the 
liquids  themselves.     Suppose  that  we  have  three  vessels  filled 

with  water,  A,  B, 
and C  (Fig.  51),  of 
equal  depth,  and 
having  bottoms  of 
equal  areas.  It  is 
plain  that  the  bot- 
tom of  vessel  A  sus- 
tains a  pressure  equal  to  the  weight  of  the  column  of  water 
abed,  or  just  the  weight  of  the  water  in  the  vessel.  The  pres- 
sure on  7y,  a  portion  of  the  bottom  of  vessel  B,  is  equal  to  the 
weight  of  a  column  of  water  ghji.  But  this  pressure  is  trans- 
mitted undiminished  to  the  surface  fh ;  consequently,  the 
pressure  on  fh  is  equal  to  the  weight  of  a  column  of  water  of 
the  size  of  efhg,  and  the  pressure  on  jl  is  equal  to  the  weight  of 
a  column  ijlk.  Hence  the  pressure  on  the  whole  bottom  fl  is 
equal  to  the  pressure  of  a  column  of  water  eflk,  or  the  same 
as  the  pressure  on  the  bottom  of  vessel  A.  But  the  weight  of 
the  water  in  B  is  less  than  the  weight  of  the  water  in  A.  Hence, 
(1)  the  pressure  on  the  bottom  of  a  vessel  may  be  greater  than  the 
weight  of  the  water  in  the  vessel. 

In  vessel  C,  the  side  mq  sustains  the  downward  pressure  of 
the  body  of  water  mqn  ;  and  the  side  pr  sustains  the  pressure  of 
the  body  orp;  while  the  bottom  qr  sustains  only  the  pressure 
of  the  column  nqro,  which  is  equal  to  the  pressure  on  the  bot- 
toms of  each  of  the  vessels,  A  and  B.  Hence,  (2)  the  pressure 
on  the  bottom  of  a  vessel  may  be  less  than  the  weight  of  the  water 
in  the  vessel. 

We  conclude,  therefore,  that  (3)  the  pressure  on  the  bottom 
of  a  vessel  depends  on  the  depth  and  area  of  the  bottom  and 
the  density  of  the  liquid,  and  is  independent  of  the  shape  of  the 
vessel  and  the  quantity  of  liquid.  —  The  important  fact  that  the 
pressure  on  the  bottom  does  not  depend  on  the  shape  of  the 
vessel  is  often  called  the  hydrostatic  paradox,  because,  though 
true,  it  seems  at  first  absurd. 


PRESSURE  IN  FLUIDS  DUE  TO   GRAVITY. 


67 


Experiment.  The  last  conclusion  may  be  verified  with  apparatus 
like  that  represented  in  Figure  52.  Vessels  A,  B,  and  C  have  different 
capacities,  but  equal  depths,  and  the  disk  d  is  to  serve  successively 
for  the  bottom  of  Fig.  52. 

each.  Each  vessel, 
when  in  use,  is  sup- 
ported by  the  tripod 
e.  The  disk  is  sup- 
ported and  pressed 
up  strongly  against 
the  bottom  of  the 
vessel  by  means  of 
a  string  passing  up 
through  the  vessel, 
and  attached  to  a 
spring-balance.  Let 
water  be  poured  in- 
to vessel  C,  and  reg- 
ulate at  pleasure  the 
amount  of  down- 
ward pressure  nec- 
essary to  push  the 
bottom  off  and  al- 
low the  water  to 
escape.  Note  the 
depth  of  water 
when  the  bottom  is 
forced  off,  and  mark  the  level  of  the  surface  with  the  pointer/.  Also 
note  the  pressure  indicated  by  the  index  of  the  balance.  Substitute 
vessel  A  for  vessel  C.  Pour  the  water  caught  in  the  basin  g,  in  the 
last  experiment,  into  vessel  A,  till  it  reaches  the  pointer  /,  when  the 
bottom  will  be  forced  off  at  the  same  depth  as  before,  as  shown  by  the 
pointer,  and  by  the  same  pressure,  as  shown  by  the  spring-balance. 
But  much  less  water  is  required  than  was  used  with  the  vessel  C.  The 
experiment,  repeated  with  vessel  B,  will  give  the  same  results  with  the 
use  of  a  still  less  quantity  of  water. 

(4)  The  pressure  due  to  gravity  on  any  portion  of  the  bottom, 
of  a  vessel  is  equal  to  the  weight  of  a  column  of  that  liquid  whose 
base  is  the  area  of  that  portion  of  the  bottom  pressed  upon,  and 
whose  hight  is  the  greatest  depth  of  the  water  in  the  vessel.  Thus, 


68  DYNAMICS. 

suppose  the  area  of  hj,  of  the  bottom  of  vessel  B  (Fig.  51),  is 
100qcm,  and  the  depth  gh  is  9cm ;  then  the  column  ghji  contains 
900ccm.  And,  since  the  weight  of  one  cubic  centimeter  of  water 
is  one  gram,  the  weight  of  the  column  is  900g,  which  is  the 
pressure  on  the  surface  hj;  and  the  pressure  on  each  of  the 
equal  surfaces  fh  and  jl  being  the  same  as  on  hj,  the  pressure 
on  the  entire  bottom  is  2700g. 

Evidently  the  lateral  pressure  at  any  point  of  the  side  of  a 
vessel  depends  upon  the  depth  of  that  point;  and,  as  depth 
at  different  points  of  a  side  varies,  hence,  (5)  to  Jlnd  the  pres- 
sure upon  any  portion  of  a  side  of  a  vessel,  we  Jlnd  the  weight  of 
a  column  of  water  whose  base  is  the  area  of  that  portion  of  the 
side,  and  whose  hight  is  the  average  depth  of  that  portion.  Thus, 
we  compute  the  pressure  on  the  side  ab  of  vessel  A  (Fig.  51), 
by  multiplying  the  area  of  the  side  90qcm  (dimensions,  9  x  10cm), 
by  the  depth  to  the  middle  point  x,  4£cm,  and  this  by  the  weight 
of  I0*510  of  water,  which  gives  405g  for  the  pressure  on  the  side 

ab. 

,- 

QUESTIONS  AND    PROBLEMS. 

1.  It  is  apparent  that  a  dam  (Fig.  53),  to  be  equally  capable  of 
resisting  pressure  in  all  its  parts,  should  be  made  thicker  towards  the 
bottom.    How  rapidly  should  its  thickness 
increase? 

2.  At  high  tide,  suppose  the  flood-gate  of 
a  dock  to  be  closed,  leaving  the  surface  of 
water  o*n  the  inside  and  outside  of  the  gate 
at  the  same  level.    From  which  does  the  gate 
sustain  the  greater  pressure,  the  water  in 
the  dock,  or  the  ocean  of  water  outside  ? 
Why? 

3.  The  interior  dimensions  of  the  rectan- 
gular vessel  (Fig.  54)  are  25cm  in  length,  20cm  in  width,  and  15cm  in 
depth.    The  vessel  is  full  of  water.     Compute  the  total  pressure  on 
each  of  the  six  sides. 

4.  Suppose  that  the  plug  n  (Fig.  54) ,  the  area  of  whose  end  is  4<icm, 
is  pressed  down  upon  the  surface  of  the  water  with  the  force  of  100s ; 
what  additional  pressure  will  each  side  of  the  vessel  sustain  ? 


THE   SURFACE   OF   A  LIQUID   AT  REST  IS   LEVEL.      69 


Fig.  54. 


5.  How  great  will  be  the  whole  pressure  that  each  side  sustains, 
due  to  the  weight  of  the  liquid  and  the  external  pressure? 

6.  Suppose  mercury,  which  is  13.6  times  heavier 
than  water,  to  be  employed  instead  of  water,  what 
would  be  the  answers  to  the  three  preceding  ques- 
tions? 

7.  Into  the  top  of  a  keg  filled  with  water,  a  brass 
tube  10m  long  is  inserted,  a  transverse  section  of 
whose  bore  is  l<icm.     The  depth  of  the  water  in  the 
cask  is  30cm,  and  the  area  of  the  bottom  of  the  cask 

is  40icm.  (a)  Compute  the  pressure  on  the  bottom  of  the  keg. 
(6)  Compute  the  pressure  on  the  bottom  of  the  cask  if  the  tube  is  filled 
with  water,  (c)  What  is  the  weight  of  the  water  in  the  tube  that 
causes  this  extra  pressure? 

8.  What  crushing-force  on  each  side  would  an  empty  cubical  box, 
the  area  of  one  of  whose  sides  is  l^m,  sustain,  if  lowered  lkm  into  the 
sea?     llftO 

9.  What  crushing-force  on  each  side  would  this  box  sustain  from 
the  atmospheric  pressure  at  the  sea-level,  if  the  air  were  completely 
exhausted  therefrom? 

10.  Suppose  the  top  of  the  vessel  (Fig.  54)  to  tee  the  weak  part  of 
the  vessel,  not  able  to  sustain  more  than  50s  pressure  on  10^cm,  what 
pressure  applied  to  the  plug  will  burst  the  vessel? 

§  56.  The  surface  of  a  liquid  at  rest  is  level.  — By  jolt- 
ing a  vessel  the  surface  of  a  liquid  in  it  may  be  made  to  assume 
the  form  seen  in  Figure  55.  Can  it  retain  this  form  ?  Take 
two  molecules  of  the  liquid  at  the  points  a 
and  6,  on  the  same  horizontal  level.  The 
downward  pressure  upon  a  is  the  weight  of 
a  column  of  molecules  ac,  and  the  downward 
pressure  upon  b  is  the  weight  of  the  column 
bd.  Now,  since  the  pressure  at- a  given  depth 
is  equal  in  all  directions,  bd  and  ac  represent 
the  lateral  pressures  at  the  points  b  and  a  respectively.  But  bd 
is  greater  than  ac ;  hence,  the  molecules  a  and  6,  and  those  lying 
in  a  straight  line  between  them,  are  acted  upon  by  two  unequal 
forces  in  opposite  directions.  There  will,  therefore,  be  a  move- 
ment of  molecules  in  the  direction  of  the  greater  force  toward 


Fig.  55. 


70  DYNAMICS. 

a,  till  there  is  equilibrium  of  forces,  which  will  only  occur  when 
the  points  a  and  b  are  equally  distant  from  the  surface ;  or,  in 
other  words,  there  will  be  no  rest  till  all  points  in  the  surface  are 
on  the  same  horizontal  level. 

This  fact  is  commonly  expressed  thus:  "Water  always  seeks  its 
lowest  level."  In  accordance  with  this  principle,  water  flows  down  an 
inclined  plane,  and  will  not  remain  heaped  up.  An  illustration  of  the 
application  of  this  principle,  on  a  large  scale,  is  found  in  the  method 
of  supplying  cities  with  water.  Figure  56  represents  a  modern  aque- 
duct, through  which  water  is  conveyed  from  an  elevated  pond  or  river 
a,  beneath  a  river  b,  over  a  hill  c,  through  a  valley  d,  to  a  reservoir  e, 
in  a  city,  from  which  water  is  distributed  by  service-pipes  to  the  dwell- 

r.  5(5. 


ings.  The  pipe  is  tapped  at  different  points,  and  fountains  rise  theo- 
retically to  the  level  of  the  water  in  the  pond,  but  practically  not  so 
high,  on  account  of  the  resistance  of  the  air  and  the  check  which  the 
ascending  stream  receives  from  the  falling  drops.  Where  should  the 
pipes  be  made  stronger,  on  a  hill  or  in  a  valley?  Where  will  water 
issue  from  faucets  with  greater  force,  in  a  chamber  or  in  a  basement? 
How  high  may  water  be  drawn  from  the  pipe  in  the  house/? 

§  57.  Artesian  wells,  etc.  — In  most  places,  the  crust  of  the 
earth  is  composed  of  distinct  layers  of  earth  and  rock  of  various  kinds. 
These  layers  fre^ently  assume  concave  shapes,  so  as  to  resemble  cups 
placed  one  within  another.  Figure  57  represents  a  vertical  section 
exposing  a  few  of  the  surface-layers  of  the  earth's  crust :  a  is  a  stratum 
of  loose  sand  or  gravel;  6,  a  clay-bed;  c,  a  stratum  of  slate;  d,  a 
stratum  of  limestone ;  the  whole  resting  on  a  bed  of  granite  e.  If  you 
hollow  out  a  lump  of  clay,  and  pour  water  into  the  cavity,  you  will 
find  that  the  water  will  percolate  through  the  clay  very  slowly.  Water 
that  falls  in  rain  passes  readily  through  the  gravel  a,  till  it  reaches  thf; 
clay-bed  6,  where  it  collects.  Hence  a  wett,  sunk  to  the  clay-bed,  will 


PARADOX.  71 

fill  with  water  as  high  as  the  water  stands  above  the  clay.  Water  also 
works  its  way  from  elevated  places  down  between  the  strata  of  rocks. 
If  a  hole  is  bored  through  the  slate  c,  water  will  rise  above  the  surface 
of  the  ground  in  a  fountain,  in  attempting  to  reach  the  level  of  its 
source  on  the  hill ;  and  if  bored  still  lower,  through  the  stratum  d,  a 
still  higher  fountain  may  result.  Such  borings  are  called  Artesian 
wells.  Water  frequently  forces  its  way  through  fissures  in  the  rocky 
strata  to  the  surface,  as  at  t,  and  gives  rise  to  springs. 

Fig.  57. 


§  58.  "Any  quantity  of  liquid,  however  small,  may  bal- 
ance any  quantity  of  liquid,  however  large."  —  If  you  lead 
a  pipe  through  a  dike  by  the  seashore,  and  curve  it  upward,  the 
water  will  rise  no  higher  than  the  sea-level,  even  though  the  pipe 
should  end  in  a  quill. 

Notwithstanding  that  every-day  experience  teaches  that 
"  liquids  seek  a  level,"  it  may  seem  strange  that  the  large 
quantity  of  water  in  a  teapot  is  balanced  by  the  small  quantity 
in  the  nozzle.  Why,  for  instance,  should  the  liquid  in  the  small 
arm  B  balance  the  liquid  in  the  large  arm  A,  of  the  vessel  in 
Figure  58  ?  Imagine  the  liquid  in  A  to  be  divided  into  columns 
a,  6,  c,  and  d,  each  equal  to  the  column  e.  It  is  clear  that  the 
downward  pressure  of  any  one  of  the  columns  a,  6,  c,  d,  or  e, 
will  balance  the  downward  pressure  of  any  one  of  the  other 
columns,  and  that  there  is  no  reason  why  e  should  rise  above 
any  one,  or  all,  of  the  others. 


72  DYNAMICS. 

§  59.  Siphon.  —  A  siphon  is  an  instrument  used  for  trans- 
ferring a  liquid  from  one  vessel  to  another  through  the  agency 
of  atmospheric  pressure.  It  consists  of  a  tube  of  any  material 
(rubber  is  often  most  convenient) ,  bent  into  a  shape  somewhat 
like  an  inverted  U.  To  set  it  in  ope- 
ration, fill  the  tube  with  a  liquid,  stop 
each  end  with  a  finger  or  cork,  insert 
one  end  in  the  liquid  to  be  transferred, 
bring  the  other  end  below  the  level  of 
the  surface  of  the  liquid,  remove  the 
stoppers,  and  the  liquid  will  immedi- 
ately flow.  Why  ?  The  force  that 
raises  the  liquid  in  the  short  arm  of  the 
siphon  A  (Fig.  59)  is  the  pressure  of 
the  atmosphere  less  the  downward  pressure  of  a  column  of  water 
dc.  The  excess  tends  to  carry  the  water  over  through  the  bend. 
On  the  other  hand,  the  upward  pressure  at  6,  tending  to  carry 
the  water  back  into  the  vessel,  is  an  atmosphere  less  the  weight 
of  a  column  of  water  ba.  But  the  former  excess  is  greater  than 
the  latter  by  the  weight  of  a  column  eb  ;  consequently  the  liquid 
moves  in  the  direction  of  the  greater  force  towards  6,  with  a 
velocity  dependent  on  the  distance  eb.  When  the  distance  eb 
becomes  zero,  as  in  B,  the  flow  ceases,  and  the  liquid  stands  in 
the  tube. 

If  one  of  the  vessels  is  raised  a  little,  as  in  C,  the  liquid  will 
flow  from  the  raised  vessel,  till  the  surfaces  in  the  two  vessels 
are  on  the  same  level.  The  remaining  diagrams  in  this  cut 
represent  some  of  the  great  variety  of  uses  to  which  the  siphon 
ma}7"  be  put.  D,  E,  and  F  are  different  forms  of  siphon  fountains. 
In  D,  the  siphon  tube  is  filled  by  blowing  in  the  tube/.  Explain 
the  remainder  of  the  operation.  A  siphon  of  the  form  G  is 
always  ready  for  use.  It  is  only  necessary  to  dip  one  end  into 
the  liquid  to  be  transferred.  Why  does  the  liquid  not  flow  out 
of  this  tube  in  its  present  condition  ?  H  illustrates  the  method 
by  which  a  heavy  liquid  may  be  removed  from  beneath  a  lighter 
liquid.  By  means  of  a  siphon  a  liquid  may  be  removed  from  a 


SIPHONS. 


73 


vessel  in  a  clear  state,  without  disturbing  sediment  at  the  bot- 
tom. I  is  a  Tantalus  cup.  A  liquid  will  not  flow  from  this 
cup  till  the  top  of  the  bend  of  the  tube  is  covered.  It  will  then 
continue  to  flow  as  long  as  the  end  of  the  tube  is  in  the  liquid. 
The  siphon  J  may  be  filled  with  a  liquid  that  is  not  safe  or 


Fig.  59. 


pleasant  to  handle,  by  placing  the  end  j  in  the  liquid,  stopping 
the  end  fc,  and  sucking  the  air  out  at  the  end  I  till  the  lower  end 
is  filled  with  the  liquid. 

Gases  heavier  than  air  may  be  siphoned  like  liquids.   Vessel  o 


74        .  DYNAMICS. 

contains  carbonic-acid  gas.  As  the  gas  is  siphoned  into  the 
vessel  p,  it  extinguishes  a  candle-flame.  Gases  lighter  than 
air  are  siphoned  by  inverting  both  the  vessels  and  the  siphon. 

QUESTIONS. 

1.  What  is  the  greatest  hight  to  which  the  bend  r  (in  A,  Fig.  59) 
can  be  carried,  and  allow  water  to  flow  ? 

2.  What  would  be  the  greatest  hight  if  mercury  were  used  ? 

3.  Suppose  the  bejid  r  is  15m  above  the  liquid ;  what  theoretically 
ought  to  happen  when  the  end  6  is  unstopped  ? 

4.  What  would  happen  if  the  long  arm  were  cut  off  at  e  ? 

5.  What  would  happen  if  it  were  cut  off  between  e  and  a  ? 

6.  What  would  happen  if  the  siphon  were  lifted  out  of  the  liquid  ? 

7.  What  would  be  the  effect  of  lengthening  the  long  arm  ? 

8.  Must  the  two  arms  of  a  siphon  be  of  unequal  length? 

9.  How  far  can  a  liquid  be  carried  by  a  siphon  ? 

10.  Will  a  siphon  work  in  a  vacuum  ?     * 

11.  Imagine  that  some  such  condition  of  things  as  is  represented  by 
the  apparatus  K  (Fig.  59)  exists  in  the  earth,  and  that  the  siphon  a 
has  a  smaller  bore  than  the  siphon  c ;  can  you  account  for  intermittent 
springs  which  flow  and  cease  to  flow  at  nearly  equal  intervals  of  time? 

§  60.  Apparatus  for  raising  liquids.  —  The  siphon  can 

only  be  used  for  transferring  liquids  over  hights  to  a  lower 

level.      Liquids    cannot   be   transferred   to   a 

Fig.  60. 

higher  level  by  atmospheric  pressure  alone.  In 
fact,  atmospheric  pressure  is  only  a  conven- 
ience, and  never  does  work.  If  the  piston  a 
of  a  syringe  (Fig.  60)  is  raised,  the  air  is  rare- 
fied below  it,  and  the  atmospheric  pressure  will 
force  water  up  into  the  syringe  ;  but  to  raise 
the  piston,  against  the  atmospheric  pressure 
tending  to  force  it  downward,  requires  as  much 
muscular  energy  as  would  be  required  to  raise 

the  same  quant%  of  water  to  the  same  hight  as  that  to  which 

it  is  raised  in  the  syringe. 

The  common  lifting-pump  is  constructed  like  the  barrel  of 

an  air-pump.     Figure  61   represents  the  piston  in  the  act  of 


APPARATUS   FOR   RAISING  LIQUIDS.  75 

rising.     As  the  air  is  rarefied  below  it,  water  rises  by  atmos- 
pheric pressure,  and  opens  the  lower  valve.     The  weight  of  the 
water  above  the  piston  closes  the  upper  valve,  and         ^    61 
the  water  is  discharged  from  the  spout.    When  the 
piston  is  pressed  down,  the  lower  valve  closes, 
the  upper  valve  opens,  and  the  water  between  the 
bottom  of  the  barrel  and  the  piston  passes  through 
the  upper  valve  above   the  piston.      How   high 
can  the  bottom  of  the  barrel  be  above  the  surface 
of  the  liquid,  if  the  liquid  to  be  pumped  is  water  ? 
How  high  if  it  is  mercury? 

The  liquid  is  sometimes  said  to  be 
raised  in  a  lifting-pump  by  the  "  force 
of  suction."  Is  there  such  a  force? 

Experiment.  Bend  a  glass  tube  into 
a  U  shape,  with  unequal  arms,  as  in  Figure  62.  Fill  the 
tube  with  a  liquid  to  the  level  cb.  Close  the  end  b  with 
a  finger,  and  try  to  suck  the 
liquid  out  of  the  tube.  You 
find  it  impossible.  Remove 

the  finger  from  6,  and  you  can  suck  the 

liquid  out  with  ease.     Why? 

The  piston  of  a  force-pump  (Fig. 
63)  has  no  valve,  but  a  branch  pipe 
leads  from  the  lower  part  of  the  bar- 
rel to  an  air-condensing  chamber  a, 
at  the  bottom  of  which  is  a  valve  c, 
opening  upward.  As  the  piston  is 
raised,  water  is  forced  up  through  the 
valve  d,  while  water  in  a  is  prevented 
from  returning  by  the  valve  c.  When  the  piston  is  forced 
down,  the  valve  d  closes,  the  valve  c  opens,  and  water  is 
forced  into  the  chamber  a,  condensing  the  air  above  the  water. 
The  elasticity  of  the  condensed  air  forces  the  water  out  of  the 
hose  b  in  a  continuous  stream. 


76  DYNAMICS. 


V.    BUOYANT  FORCE   OF  FLUIDS. 

Experiment  1.  Gradually  lower  a  large  stone,  by  a  string  tied  to 
it,  into  a  bucket  of  water,  and  notice  that  its  weight  gradually  becomes 
less  till  it  is  completely  submerged.  Slowly  raise  it  out  of  the  water, 
and  note  the  change  in  weight  as  it  emerges  from  the  water.  Suspend 
the  stone  from  a  spring  balance,  weigh  it  in  air  and  then  in  water,  and 
ascertain  its  loss  of  weight  in  the  latter.  Repeat  the  experiment  with 
pieces  of  iron,  wood,  and  other  substances.  Inflate  a  bladder,  and 
force  it  beneath  a  surface  of  water.  Fill  a  thin  rubber  balloon  with 
coal-gas,  and  it  will  rise  to  the  top  of  the  room. 

In  all  these  experiments  it  seems  as  if  something  in  the  fluid, 
underneath  the  articles  submerged,  were  pressing  up  against 
them.  This  lifting-force  is  called  the  buoyant  force  of  .fluids. 
Every  body  immersed  appears  to  lose  part  of  its  weight ; 
some  bodies  appear  to  lose  all  their  weight.  Do  bodies  really 
lose  any  portion  of  their  weight  when  immersed  in  a  liquid? 

Experiment  2.  Place  a  beaker  of  water  on  a  scale-pan  of  a  balance- 
beam,  and  weigh.     Weigh  a  stone  first  in  the  air,  then  in  water,  and 
F.    w  ascertain   the   apparent   loss .  of  weight. 

Then  suspend  the  stone  from  a  support 
(Fig.  64) ,  and  weigh  the  beaker  of  water 
with  the  stone  immersed,  and  it  will  be 
found  that  the  beaker  and  its  contents  gain 
in  weight  precisely  as  much  as  the  stone 
loses.  That  is,  the  water  supports  what  is 
not  supported  by  the  string,  and  no  weight 
is  really  lost.  Repeat  the  experiment  with 
a  block  of  wood. 

Experiment  3.  Make  a  saturated  solu- 
tion of  salt  in  water.  Weigh  the  same 
stone  in  air,  fresh  water,  and  salt  water. 

The  apparent  loss  of  weight  is  greater  in  salt  than  in  fresh  water. 
Throw  a  piece  of  iron  into  mercury.  It  floats  on  the  mercury  like 
cork  on  water.  Fill  a  vessel  with  carbonic-acid  gas;  blow  a  soap- 
bubble,  and  drop  it  into  the  vessel.  It  will  not  sink  in  the  vessel,  but 
rolls  over  the  side  and  falls  to  the  floor.  It  appears  that  some  fluids 
have  greater  buoyant  force  than  others.  The  water  of  the"  Dead  Sea, 
in  Palestine,  is  so  salt  (i.e.,  so  heavy)  that  a  person  could  not  possibly 
sink  in  it. 


WHY  A  SOLID   IS   BUOYED   UP  BY  A  FLUID,   ETC.     77 

§  61.  Why  a  solid  is  buoyed  up  by  a  fluid,  and  with 
how  great  a  force  it  is  buoyed  up.  —  Suppose  dcba  (Fig. 
65)  to  be  a  cubical  block  of  marble  immersed  in  a  liquid.  It  is 
obvious  that  the  downward  pressure  upon  Fig, 

the  surface  da  is  equal  to  the  weight  of  the 
column  of  liquid  edao.     The  upward  pres- 
sure   on    the    surface    cb    is    equal   to   the 
weight  of  a  column  of  liquid  ecbo.     The  dif- 
ference between  the  upward  pressure  against 
cb  and  the  downward  pressure  on  da,  is  the 
weight  of  a  column  of  liquid  ecbo  less  the 
weight  of  a  column  of  liquid  edao,  which  is 
a  column  of  liquid  dcba  (ecbo  —  edao  =  dcba} . 
But  a  column  of  liquid  dcba  has  precisely 
the  volume  of  the  solid  submerged.    Therefore,  a  solid  is  buoyed 
up  by  a  fluid  in  consequence  of  the  unequal  pressures  upon  its  top 
and  bottom  at  their  different  depths,  and  the  amount  of' the  buoyancy 
is  the  weight  of  a  body  of  Fiir  w 

that  fluid  equal  in  volume 
to  the  solid  immersed.  The 
last  proposition  is  gener- 
ally stated  as  follows  :  A 
solid  loses  in  weight  as 
much  as  the  weight  of  the 
fluid  it  displaces. 


Experiment  4.  The  last 
statement  may  be  verified 
with  apparatus  like  that 
shown  in  Figure  66.  Fill  the 
vessel  A  till  the  liquid  over- 
flows at  E.  After  the  over- 
flow ceases,  place  a  vessel  c 
under  the  nozzle.  Suspend 
a  stone  from  the  balance-beam  B,  and  weigh  it  in  air,  and  then 
carefully  lower  it  into  the  liquid,  when  some  of  the  liquid  will  flow 
into  the  vessel  c.  The  vessel  c  having  been  weighed  when  empty, 


78  DYNAMICS. 

weigh  it  again  with  its  liquid  contents,  and  It  will  be  found  that  its 
increase  in  weight  is  just  equal  to  the  loss  of  weight  of  the  stone. 

Experiment  5.  Next  suspend  a  block  of  wood  that  will  float  in 
the  liquid,  and  weigh  it  in  air.  Then  float  it  upon  the  liquid,  and 
weigh  the  liquid  displaced  as  before,  aud  it  will  be  found  that  the 
weight  of  the  liquid  displaced  is  just  equal  to  the  weight  of  the  block 
in  air. 

Hence,  a  floating  mass  displaces  its  own  weight  of  liquid;  in 

other  words,  a  floating  mass  will 
sink  till  it  displaces  an  equal 
weight  of  the  liquid,  or  till  it 
reaches  a  deptli  where  the  buoyant 
force  is  equal  to  its  own  weight. 


Experiment  6.  Next,  partially 
fill  with  water  a  glass  (Fig.  67), 
graduated  in  cubic  centimeters  and 
fractions  of  the  same.  Note  the 
level  of  the  water.  Drop  one  of  the  solids  into  the  water,  and  note 
again  the  level  of  the  water.  The  difference  between  the  two  levels 
is  the  number  of  cubic  centimeters  of  water  that  the  solid  displaces. 
But  one  cubic  centimeter  of  water  weighs  one  gram.  Hence,  the 
number  of  cubic  centimeters  displaced  is  equal  to  the  weight  in  grams 
of  the  water  displaced,  and  this  is  the  loss  in  weight  the  solid  sustains 
in  water. 

There  is  an  adage  that  "a  pound  of  feathers  weighs  more 
than  a  pound  of  gold."     Is  there  truth  in  the  statement? 

Experiment  7.  Instead  of  feathers,  we  will  employ  a  hollow  globe 
a  (Fig.  G8) ;  in  place  of  the  "  pound  of  gold,"  we  will          Fig  gg 
use  a  counterpoise  b,  of  any  metal  whose  weight  is 
just  equal  to  the  weight  of  the  globe.      Then,  when 
the  globe  and  counterpoise  are  suspended  from  the 
opposite  arms   o'f  the  balance-beam  c,  the  beam  will 
be  horizontal.      Now  place  the  whole  on  the  plate 
of  an  air-pump,  cover  with  a  receiver,  and  exhaust  the 
air.     As  soon  as  the  exhaustion  commences,  the  globe 
begins  to  descend,  and  at  the  end  of  the  operation  the  beam  is  com- 
pletely tilted.     Although  the  globe  and  counterpoise  were  both  buoyed 
up  by  the  air,  it  becomes  evident,  when  this  support  is  removed,  that 


DENSITY  AND   SPECIFIC   GRAVITY.  79 

the  globe  was  buoyed  up  more  than  the  counterpoise,  as  we  might 
expect  from  the  fact  that  it  displaces  more  air. 

A  pound  of  feathers  displaces  more  air  than  a  pound  of  gold, 
and  is  therefore  buoyed  up  more  by  the  air ;  consequently  the 
pound  of  gold,  which  balances  a  pound  of  feathers  in  the  air, 
does  not  balance  them  in  a  vacuum.  We  learn  from  this  experi- 
ment that  bodies  weigh  less  in  air  than  in  a  vacuum,  and  that 
we  never  learn  the  true  weight  of  a  body,  except  when  weighed 
in  a  vacuum. 

It  has  been  stated  (page  51)  that  the  density  of  the  atmosphere  is 
greatest  at  the  surface  of  the  earth.  A  body  free  to  move  cannot  dis- 
place more  than  its  own  weight  of  a  fluid ;  therefore  a  balloon,  which  is 
a  large  bag  filled  with  a  gas  about  fourteen  times  lighter  than  air  at  the 
sea-level,  will  rise  till  the  balloon,  plus  the  weight  of  the  car  and  cargo, 
equals  the  weight  of  the  air  displaced.  The  aeronaut,  wishing  to 
ascend  still  higher,  throws  out  a  portion  of  his  cargo;  wishing  to 
descend,  he  allows  some  of  the  gas  to  escape  at  the  top  of  the  balloon 
by  means  of  a  valve,  which  he  controls  by  means  of  a  cord  passing 
through  the  balloon  to  the  car. 

QUESTIONS. 

1.  Why  is  it  difficult  to  stand  in  water  reaching  the  neck  ? 

2.  Why  can  a  person  raise  a  stone  under  water,  which  he  cannot 
lift  when  out  of  water  ? 

3.  A  piece  of  cork  weighs  50&;  what  weight  of  water  does  it  dis- 
place when  floating  ? 

4.  What  weight  of  mercury  will  a  piece  of  iron  weighing  500«  dis- 
place ? 

VI.    DENSITY  AND   SPECIFIC   GRAVITY. 

§  62.  Density.  —  We  speak  of  a  piece  of  cork  as  being 
heavier  than  a  nail,  at  the  same  time  that  we  speak  of  cork  as 
light  and  iron  as  heavy.  This  seeming  contradiction  is  ac- 
counted for  by  the  different  meanings  which  we  attach  to  the 
terms  light  and  heavy.  In  both  cases,  light  and  heavy  are  used 
as  terms  of  comparison.  In  the  former  instance,  we  compare 


80  DYNAMICS. 

the  weights  of  the  two  particular  bodies,  without  reference  to 
volume  ;  in  the  latter,  we  call  cork  light  and  iron  heavy,  having 
no  particular  bodies  in  view,  but  because  we  know  by  experience 
that  cork  is  not  so  dense  as  iron ;  i.e.,  a  given  volume  of  cork 
contains  less  matter  than  an  equal  volume  of  iron.  The  term 
weight  refers  simply  to  the  number  of  grams,  kilograms,  etc., 
that  a  particular  body  weighs  without  reference  to  the  material 
or  the  volume.  'The  density  of  a  body  can  be  stated  only  by 
expressing  (or  understanding)  two  quantities,  viz.,  mass  and 
volume.  For  example,  suppose  that  a  block  of  wood  measures 
2  x  10  X  20cm  and  has  a  mass  of  (i.e.,  weighs)  300g ;  its  density  is 
then  X1QX20  =  tolS  =  ^'^  gram  Per  cubic  centimeter.  When 
we  speak  of  cork  as  lighter  than  iron,  it  is  evident  that  we  are 
comparing  the  densities  of  these  two  substances. 

§  63.  Specific  gravity.  —  The  specific  gravity  of  a  substance 
is  the  ratio  of  the  density  of  that  substance  to  the  density  of  another 
substance  assumed  as  a  standard;  in  other  words,  it  is  the  num- 
ber which  expresses  how  many  times  heavier  a  certain  volume  of 
a  given  substance  is  than  an  equal  volume  of  another  substance. 

To  facilitate  comparison  of  densities,  uniform  standards  are 
adopted.  Distilled  water  at  its  maximum  density,  at  4°  C.,  is 
the  standard  of  specific  gravity  for  all  solids  and  liquids.  In- 
asmuch as  one  cubic  centimeter  of  water  weighs  one  gram, 
when  the  weigh*  of  one  cubic  centimeter  of  any  substance  is  given 
in  grams,  i.e.,  when  its  density  is  given  in  its  usual  metric 
units,  the  same  number  also  expresses  its  specific  gravity. 
Thus  one  cubic  centimeter  of  water  weighs  one  gram  ;  hence  1 
is  the  specific  gravity  of  water.  The  density  of  silver  is  10.53g 
per  cubic  centimeter;  hence  the  specific  gravity  of  silver  is 
10.53.  The  standard  for  gases  is  air  at  the  average  sea- 
level  density,  and  at  a  temperature  of  0°  C.  The  weight  of  one 
cubic  centimeter  of  air,  under  these  conditions,  is  0.0012932g, 
or  about  y^  of  the  weight  of  one  cubic  centimeter  of  water. 

Let  G  =  the  specific  gravity  of  a  substance  ;  D  =  its  density 


SPECIFIC   GRAVITY. 


81 


in  grams  per  cubic  centimeter ;  V  =  the  volume  of  a  given  body 
of  it  in  cubic  centimeters ;  W  =  the  weight  of  the  given  body 
in  grams  ;  W  =  the  weight  in  grams  of  an  equal  volume  of  the 

W 

standard.     Then,  as  shown  above,  D  =  — ,  and,  by  definition, 

W 

Gr  —  — |  •     G  is  numerically  equal  to  D,  and  W  to  V. 

Since  the  loss  of  weight  of  a  solid  immersed  in  a  liquid  is 
just  the  weight  of  an  equal  volume  of  that  liquid,  it  is  evident 
that,  if  we  divide  the  weight  of  a  solid  in  air  by  its  loss  in  weight 
when  immersed  in  water,  the  quotient  will  be  its  specific  gravity. 

Experiment  1.  Obtain  small  lumps  of  glass,  iron,  lead,  marble, 
granite,  etc.,  and  weigh  each  in  air.  Partly  fill  with  water  a  measur- 
ing-beaker graduated  in  cubic  centimeters,  and  note  the  level  of  the 
water.  Drop  a  lump  into  the  water,  and  note  the  level  again.  The 
rise  of  water,  as  indicated  by  the  graduated  scale,  gives  the  volume 
(V)  of  the  specimen.  With  these  data  find  the  density  (D) ,  employing 

the  formula  D  =  — .    Next  weigh  each  of  these  lumps  submerged  in 

water,  and  find  its  loss  in  weight ;  and,  from  the  data  obtained,  ascer- 

TVr 
tain  G  from  the  formula  G  =  — f .    Prepare  blanks,  and  tabulate  year 

results  thus :  — 


Name  of 
Substance. 

W 

g 

V 

ccm 

D 

or  G 

e 

W 

g 

Win 
water. 

g 

W 
g 

G 
or  D 

e 

Av. 

e 

Flint  glass. 

435 

134 

3.24 

.09- 

435 

305 

130 

3.34 

.01+ 

3.29 

.04- 

82  DYNAMICS. 

When  the  result  obtained  differs  from  that  given  in  the  table  of  spe- 
cific gravities  (see  Appendix,  page  402),  the  difference  is  recorded  in 
the  column  of  errors  (e).  When  the  former  is  greater  than  the  latter,  it 
is  indicated  by  a  plus  sign  affixed  to  the  number;  when  less,  by  the 
minus  sign.  The  results  recorded  in  the  column  of  errors  are  not  nec- 
essarily real  errors ;  they  may  indicate  the  degree  of  impurity,  or  some 
peculiar  physical  condition,  of  the  specimen  tested. 

Experiment  2.  Obtain  good  specimens  of  cork,  oak,  elm,  and  poplar 
woods,  all  of  which  float  on  water.  Tie  to  a  specimen  a  piece  of  lead 
heavy  enough  to  sink  it;  immerse  the  two,  thus  attached,  in  a  measur- 
ing-glass, and  find  the  number  of  cubic  centimeters  of  water  displaced  by 
them.  In  the  same  way  find  the  amount  displaced  by  the  lead  alone. 
Subtract  the  amount  displaced  by  the  lead  from  the  amount  displaced  by 
the  two,  and  the  remainder  will  be  the  amount  displaced  by  the  specimen. 
Then,  regarding  the  number  of  centimeters  of  water  displaced  as  so 

W 

many  grams,  apply  the  formula  G  =  — . 

Example.  Find  the  specific  gravity  of  a  piece  of  elm  wood.  At- 
tach to  it  a  piece  of  lead  weighing  (say)  40s. 

The  combined  solids  displace 28.5s  of  water. 

The  lead  displaces 3.5s         " 

The  elm  displaces 25.0s         " 

The  elm  weighs  in  air 20.  OS         " 

The  specific  gravity  of  elm  wood  is   .     .     .  20.0  -f-  25  =  .8. 

Experiment  3.  Find  the  specific  gravity  of  alcohol,  a  saturated  so- 
lution of  common  salt,  sea-water,  naphtha,  olive-oil,  pure  milk,  and 
mercury  in  the  following  manner :  ascertain  the  loss  in  weight  of  a 
sinker  in  each  one  of  these  liquids,  also  in  water,  and  then  apply  the 

W 

formula  G  =  — , .    Here  W  and  W  represent  the  loss  of  weight  of  the 

sinker  in  the  liquid  and  water  respectively. 

Example.  Compute  the  specific  gravity  of  alcohol  from  the  follow- 
ing data :  — 

A  piece  of  marble  weighs  in  air  ....  56.80s 
The  same  weighs  in  water 36.808 

Loss  in  water 20.00s 

56.808 
The  marble  weighs  in  alcohol 4Q..96g 

Loss  in  alcohol .   15.84s 


HYDROMETERS.  83 


Since  20«  and  15.84s  are  the  weights  respectively  of  equal  volumes  of 
a,ter  and  alcohol, 
gravity  of  alcohol. 


water  and  alcohol,  and  since  G=— ,,then  -^—=.792,  the  specific 


§  64.    Hydrometers.  —  Experiment.    Take  a  uniform  rod  of 
light  wood  about  a  foot  long,  and  mark  off  on  it  a  scale  of  equal  parts. 
A  convenient  size  is  \  inch  square,  and  a  suitable  scale  is     Fig.  69. 
inches  and  half  inches.     Coat  the  rod  with  paraffine  to  pre- 
vent its  absorbing  water  and  swelling.     Bore  into  the  end 
marked  zero  a  hole  about  2  inches  deep,  and  drive  in  bullets 
till  the  rod  will  sink  in  water  (Fig.  69)  just  to  some  inch- 
mark,  and  stop  the  end  with  paraffine.     If  it  sinks  too  deep, 
cut  off  the  upper  end  of  the  rod. 

Suppose  the  rod  sinks  8  inches  in  water ;  then,  if  it  is  \  inch 
square,  it  displaces  2  cu.  in.  of  water.  The  weight  of  the 
water  displaced  must  just  equal  the  weight  of  the  rod  (see 
page  78).  Now  immerse  it  in  alcohol;  it  sinks  deeper,  say  to 
the  10-inch  mark ;  that  is,  -V°-  cu.  in.  of  alcohol  weigh  the  same 

V      8 
as  |  cu.  in.  of  water;   therefore,  G  =  — =— =  .800.    If  in 

brine  it  sinks  only  6f  in.,  G  =  j-2  =  1.20. 

Apparatus  like  that  described  is  called  a  hydrometer.  In- 
stead of  a  rod  of  wood,  a  glass  tube  is  generally  used,  ter- 
minating in  a  bulb  containing  shot  or  mercury.  The  tube 
contains  a  scale  with  numbers  corresponding,  which  express  the  specific 
gravity,  so  that  no  computation  is  necessary.  Make  solutions  of 
various  substances,  and  test  their  specific  gravity  with  your  hydrome- 
ter, and  test  the  accuracy  of  the  results  so  obtained  by  other  processes. 

The  most  direct  way  of  finding  the  specific  gravity  of  liquids 
and  gases  is  by  employing  vessels  that  hold  definite  weights  of 
the  two  standards,  water  or  air,  and  then  weighing  these  vessels 
when  filled  with  other  liquids  or  gases  ;  and,  after  deducting  the 

W 

weight  of  the  vessel,  applying  the  formula,  G  =  — -• 

The  specific  gravity  of  a  solid  that  is  dissolved  by  water  may 
be  found  b}^  weighing  it  in  a  liquid  that  will  not  dissolve  it 
(e.g.,  rock-salt  in  naphtha);  and,  having  found  its  specific 


84  DYNAMICS. 

gravity  as  compared  with  the  liquid  used,  multiply  this  result  by 
the  specific  gravity  of  the  liquid. 

W  W 

From  the  formula  D  =  — ,  we  have  V  =  —  ;  hence,  the  volume 

of  an  irregular-shaped  body  may  be  found  in  cubic  centimeters  by 
dividing  its  weight  in  grams  by  its  density. 

W 

Again,  from  the  formula  D  =  — ,  we  have  W= V  x  D.  Hence, 

when  the  volume  and  density  of  a  body  are  known,  its  weight  in 
grams  may  be  found  by  multiplying  its  volume  in  cubic,  centime- 
ters by  its  density. 

QUESTIONS  AND   PROBLEMS.1 

1.  How  high  can  sulphuric  acid  be  raised  by  a  lifting-pump? 

2.  What  is  the  weight  of  50s  of  water  in  water? 

3.  Find  the  specific  gravity  of  wax  from  the  following  data :  weight 
of  a  given  mass  of  wax  in  air  is  80«;  wax  and  sinker  displace  102.88ccm 
of  water ;  sinker  alone  displaces  I4ccm. 

4.  Why  does  a  light  liquid  (e.gr.,  oil),  introduced  under  a  heavier 
liquid  (e.g.,  water),  rise? 

5.  Glass  is  about  three  times  heavier  than  water;  how,  then,  can  a 
glass  tumbler  float  in  water? 

6.  How  can  iron  vessels  float  in  water? 

7.  A  block  of  ice  containing  500ccm  is  floating  on  water ;  how  many 
cubic  centimeters  are  out  of  water? 

8.  Will  ice  float  or  sink  in  alcohol? 

9.  How  much  more  matter  is  there  in  500ccm  of  sea-water  than  in 
the  same  volume  of  fresh  water? 

10.  In  50k  of  gold  how  many  cubic  centimeters? 

11.  What  is  the  density  of  gold? 

12.  What  is  the  density  of  cork? 

13.  What  is  the  density  of  air  at  ordinary  pressure,  and  at  a  tempera 
ture  of  0°  C? 

14.  An  irregular  piece  of  marble  loses  53&  when  weighed  in  water. 
How  many  cubic  centimeters  does  it  contain? 

15.  When  will  a  body  sink,  and  when  float? 

16.  How  many  cubic  centimeters  of  air  at  the  sea-level  does  it  takt 
to  weigh  as  much  as  lccm  of  water? 

1  Consult  the  Tables  of  Specific  Gravities,  in  the  Appendix,  Section  C. 


QUESTIONS   AND  PROBLEMS.  85 

17.  How  much  will  lk  of  copper  weigh  in  water? 

18.  What  does  a  piece  of  lead  20  X  10  X  5cm  weigh? 

19.  What  will  it  weigh  in  water? 

20.  What  will  it  weigh  in  mercury? 

21.  What  becomes  of  the  weight  that  is  lost? 

22.  If  15s  of  salt  be  dissolved  in  I1  of  water,  without  increasing  the 
volume  of  the  liquid,  what  will  be  the  specific  gravity  of  the  solu- 
tion? 

23.  A  mass  of  lead  weighs  lk  in  air.    What  will  it  weigh  in  a 
vacuum? 

24.  A  mass  whose  weight  in  air  is  30s,  weighs  in  water  26s,  and  in 
another    liquid    27?.      What    is    the    specific    gravity    of  the    other 
liquid? 

25.  A  silver  spoon,  weighing  150s,  is  supported  by  a  string  in  water. 
What  part  of  the  weight  is  sustained  by  the  string,  and  what  part  is 
supported  by  the  water? 

26.  A  boat  displaces  25cbm  of  water.     How  much  does  it  weigh? 

27.  If  50k  of  stone  were  placed  in  the  boat,  how  much  water  would 
it  displace? 

28.  If  the  boat  is  capable  of  displacing  100cbm  of  water,  what  weight 
must  be  placed  in  it  to  sink  it? 

29.  An  empty  glass  globe  weighs  lOOS;  full  of  air  it  weighs  102.4*; 
full  of  chlorine  gas,  it  weighs  105.928«.     What  is  the  specific  gravity 
of  chlorine  gas? 

30.  What  weight  of  alcohol  can  be  put  into  a  vessel  whose  capacity 
is  li. 

31.  You  wish  to  measure  out  50s  of  sulphuric  acid.     To  what  num- 
ber on  a  beaker   graduated    in    cubic   centimeters  will  that  corre- 
spond? 

32.  State  how  you  would  measure  out  80s  of  nitric  acid  in  a  measur- 
ing-beaker. 

33.  A  measuring-beaker  contains  35ccm  of  naphtha.     What  is  the 
weight  of  the  naphtha? 

34.  A  lead  pipe  is  carried  20m  below  the  surface  of  water  in  a  reser- 
voir.    What  bursting-force  per  square  centimeter  must  it  be  capable  of 
sustaining? 

35.  A  cubical  vessel,  each  of  whose  sides  contains  2500icm,  is  filled 
with  water.    What  pressure  does  its  bottom  sustain?    One  of  its  sides? 

36.  A  solid  floats  at  a  certain  depth  in  a  liquid  when  the  vessel 
which  contains  it  is  in  the  air ;  if  the  vessel  is  placed  in  a  vacuum,  will 
the  solid  sink,  rise,  or  remain  stationary? 


86  DYNAMICS. 

VII.    MOTION. 

§  65.  Motion  and  rest  relative  terms. — To  a  person 
riding  in  a  railway  car,  and  confining  his  attention  to  objects 
in  the  car,  everything  appears  to  be  at  rest ;  but  let  him  direct 
his  attention  to  objects  by  the  wayside,  and  at  once  he  discovers 
that  all  in  the  car  are  in  motion.  Matter  may  be  at  rest  with 
reference  to  certain  objects,  and  in  motion  in  regard  to  others. 
Motion  and  rest  are  wholly  relative  terms,  and  inapplicable  to  an 
object  considered  apart  from  all  others.  We  cannot  locate  an 
object  except  with  reference  to  another  object,  nor  can  we  con- 
ceive of  change  or  permanence  of  position  of  an  object,  except 
in  relation  to  some  other  object.  The  aeronaut,  moving  at  the 
rate  of  sixty  miles  an  hour,  knows  not  that  he  is  moving  at  all, 
till  he  looks  away  from  his  balloon,  and  sees  cities  and  towns 
passing  in  panorama  bei>eath  him. 

§  66.  All  matter  is  in  motion.  —  There  is  no  such  thing  as 
absolute  rest  in  the  universe.  There  is  no  use  for  the  word  rest,  ex- 
cept to  indicate,  with  reference  to  each  other,  the  condition  of 
objects  that  are  moving  in  the  same  direction  and  with  the 
same  velocuVv.  For  example,  a  span  of  horses  drawing  a  car- 
riage, at  the  rate  of  ten  miles  an  hour,  are  at  rest  with  reference 
to  each  other  and  the  carriage.  The  stars,  that  compose  the 
heavenly  constellations,  maintain  punctiliously  their  relative 
positions,  while  they  sweep  with  prodigious  velocities  through 
space.  The  phrase  "  at  rest"  can  only  be  used  in  an  extremely 
limited  sense,  and  in  common  language  refers  only  to  the  condi- 
tion of  an  object  with  reference  to  that  on  which  it  stands,  as  a 
car,  deck  of  a  ship,  or  surface  of  the  earth.  It  is  only  by  putting 
entirely  out  of  mind  the  motions  of  the  earth  that  we  can  speak 
of  any  terrestrial  object  as  being  at  rest. 

Not  only  is  there  motion  of  mass  as  a  whole,  or  visible  me- 
chanical motion,  but  there  is  a  motion  of  the  molecules  within 
the  mass,  —  an  invisible  molecular  motion  called  heat.  We 
cannot  see  the  movements  of  the  molecules  of  steam,  but  we 


VELOCITY.  87 

know  that  they  exist  by  their  great  power,  manifested  in  moving 
machinery. 

§  67.  Velocity.  —  Uniform  and  varied  motion.  —  All 
motion  takes  time ;  hence  the  term  velocity,  which  refers  to  the 
space  traversed  in  a  unit  of  time.  Motion  may  be  uniform  or 
varied :  uniform,  when  an  object  traverses  successively  equal 
spaces  in  all  equal  intervals  of  time ;  varied,  when  unequal 
spaces  are  traversed  in  any  equal  intervals  of  time.  Varied 
motion  may  be  accelerated  or  retarded :  accelerated,  when  the 
spaces  traversed  increase  at  each  successive  interval  of  time ; 
retarded,  when  the}-  diminish.  The  motion  of  a  train  of  cars,  in 
starting  from  a  station  is  at  first  accelerated,  afterwards  tolerably 
uniform,  and  when  the  brakes  are  applied,  it  becomes  retarded. 
Strictly  speaking,  all  motions  are  varied  ;  there  is  no  illustration  of 
absolutely  uniform  motion  in  Nature  nor  in  art,  though  we  may 
conceive  of  its  possibility  and  have  very  closely  approximated  to  it. 

The  velocity  of  a  body  having  accelerated  or  retarded  motion  can 
be  given  only  at  some  definite  point  by  an  estimate  of  the  distance  it 
would  traverse  in  a  unit  of  time,  were  it  to  continue  in  uniform  motion 
at  the  speed  it  has  at  that  point.  For  instance,  a  railway  train  passes 
us,  and  we  estimate  that  its  velocity  is  30  miles  an  hour,  although  in  a 
few  minutes  its  speed  may  be  reduced  to  10  miles  an  hour,  and  a  little 
later  it  may  come  to  rest.  When  we  assign  a  velocity  of  30  miles  an 
hour,  we  have  no  thought  of  whether  it  will  run  30  miles  during  the 
next  hour,  or  whether  it  will  run  an  hour ;  we  mean  that,  should  it 
retain  its  present  speed,  it  will  be  30  miles  away  from  us  at  the  end  of  au 
hour. 

VIII.    FIRST  LAW  OF  MOTION.  —  INERTIA. 

Now,  what  is  it  that  sets  in  motion  that  which  was  previously 
at  rest?  We  may  call  it  force;  but  what  idea  does  this  term 
convey?  Let  us  question  our  own  experience.  We  leave  an 
apple  lying  upon  a  table ;  have  we  not  entire  confidence  that  it 
will  continue  to  lie  there,  unless  disturbed  by  some  other  body  ? 
If  on  returning  we  find  it  gone,  are  we  not  sure  that  it  has  been 
removed  by  the  action  of  some  body  other  than  itself?  An 


88  DYNAMICS. 

apple  falls  to  the  ground,  and  although  the  action  is  one  of  the 
most  mysterious  in  all  nature,  yet  do  we  not  almost  instinctively 
trace  the  cause  to  some  action  between  the  apple  and  the  earth  ? 
The  ball  at  rest  is  put  in  motion  by  a  bat ;  but  must  not  the  bat 
first  be  put  in  motion  ?  And  when  we  find  the  cause  of  its  mo- 
tion, is  it  not  an  antecedent  motion  in  some  other  object?  We 
conclude,  then  (1),  that  motion  cannot  originate  in  an  object 
isolated  from  all  others,  but  it  always  arises  from  MUTUAL  action 
between  at  least  two  bodies. 

Again,  the  bat,  having  received  motion,  is  capable  of  impart- 
ing motion  to  the  ball ;  but,  having  set  in  motion  one  ball,  is  it 
equally  capable  of  putting  in  motion  another  ball  ?  Can  a  mass 
impart  motion  and  retain  all  its  motion?  Is  it  not  like  a  com- 
mercial transaction,  a  trade,  to  which  there  are  two  parties,  one 
a  buyer  and  the  other  a  seller?  that  is,  are  not  all  transactions 
between  the  parties  (i.e.,  the  mover  and  the  moved)  of  the  na- 
ture of  a  transfer,  which  should  be  entered  on  the  debit  side  of 
one's  account,  and  the  credit  side  of  the  other's?  We  conclude 
(2)  that  motion  in  one  body  is  caused  only  by  another  body's 
parting  with  some  of  its  power  of  producing  motion. 

If  a  sled,  on  which  a  child  is  sitting,  is  suddenly  put  in  mo- 
tion, the  child  is  left  in  the  place  from  which  the  sled  started. 
If  the  child  and  sled  are  both  in  motion,  and  the  sled  is  sud- 
denly stopped,  the  child  lands  some  distance  ahead.  If  the 
sled  is  started  slowty,  the  child  partakes  of  the  motion  of  the 
sled,  and  is  carried  along  with  it;  and  if  the  sled  gradually 
stops,  the  child's  motion  is  gradually  checked,  and  it  retains  its 
place  on  the  sled.  This  shows  (3)  that  masses  of  matter  receive 
motion  gradually  and  surrender  it  gradually. 

Even  very  small  bodies  require  time  to  start  and  to  stop.  The  sand- 
blast, employed  for  engraving  figures  on  glass,  furnishes  a  fine  illus- 
tration of  this  fact.  A  box  of  fine  quartz-sand  is  placed  in  an  elevated 
position.  A  long  tube  extends  vertically  down  from  the  bottom  of  this 
box.  The  plate  of  glass  to  be  engraved  is  covered  with  a  thin  layer  of 
melted  wax.  When  cool,  the  design  is  sketched  with  a  sharp-pointed 


FIRST  LAW   OF  MOTION.  89 

instrument,  in  the  wax,  leaving  the  glass  exposed  only  where  the  lines 
are  traced.  The  plate  is  then  placed  beneath  the  orifice  of  the  tube, 
and  exposed  to  a  shower  of  sand.  The  velocity  of  the  sand-grains  is 
not  at  its  maximum  at  the  start,  but  is  constantly  accelerated  till  they 
reach  the  plate,  where  their  velocity  in  turn  is  gradually  given  up. 
The  wax,  on  account  of  its  yielding  nature,  gradually  brings  them  to 
rest;  but  the  glass,  notwithstanding  its  hardness,  cannot  stop  them 
quite  at  its  surface ;  and,  therefore,  it  suffers  a  chipping  action  from 
the  sand.  Thus  the  soft  wax  affords  a  protection  from  the  action  of 
the  falling  sand  of  all  parts  except  those  intended  to  be  cut.  A  still 
greater  force  is  generally  given  to  the  sand  by  steam  blown  through 
the  tube.  For  this  reason  the  apparatus  is  called  a  sand-blast.  Hard 
metals  like  steel  are  engraved  in  the  same  manner.  Yet  the  hand 
may  be  held  in  the  blast  several  seconds  without  injury.  (What  is  the 
difference  in  the  effects  of  catching  a  base-ball  with  hands  held  rigidly 
extended,  and  allowing  the  hands  to  yield  somewhat  to  the  motion  of 
the  ball?) 

Roll  a  marble  on  a  carpet,  —  it  soon  stops  ;  roll  it  on  a  smooth 
marble  floor,  —  it  rolls  much  farther.  On  a  perfectly  smooth  sur- 
face it  might  roll  for  hours.  If  we  could  provide  such  a  surface, 
and  dispense  with  the  resistance  of  the  air,  how  long  would  it 
roll?  These  conditions  are  impracticable?  True.  But  have 
not  the  heavenly  bodies  rolled  for  millions  of  years  through  fric- 
tionless  space,  unchecked  because  unimpeded? 

Motion  unobstructed  is  perpetual.  Motion  undisturbed  is  in  a 
straight  line.  Along  which  will  a  marble  roll  more  nearly  in  a 
straight  line,  a  smooth  or  a  rough  floor?  What  if  the  floor  were 
perfectly  smooth? 

The  relations  between  matter  and  force  are  admirably  and 
concisely  expressed  in  what  are  known  as  Newton's  Three  Laws 
of  Motion. 

§  68.  First  Law  of  Motion.  —  A  body  at  rest  remains  at 
rest,  and  a  body  in  motion  moves  with  uniform  velocity  in  a 
straight  line,  unless  acted  upon  by  some  external  force  to  change 
its  condition. 

That  part  of  the  law  which  pertains  to  motion  is  briefly  summarized  in 
the  familiar  expression,  "  perpetual  motion."  "  Is  perpetual  motion  pos- 


90  DYNAMICS. 

sible?"  has  been  often  asked.  The  answer  is  simple,  —  Yes,  more  than 
possible,  necessary,  if  no  force  interferes  to  prevent.  What  has  a  person 
to  do  who  would  establish  perpetual  motion?  Isolate  a  moving  body 
from  interference  of  all  external  forces,  such  as  gravity,  friction,  and 
resistance  of  the  air.  Can  the  condition  be  fulfilled? 

In  consequence  of  its  utter  inability  to  put  itself  in  motion  or 
to  stop  itself,  every  body  of  matter  tends  to  remain  in  the  state 
that  it  is  in  with  reference  to  motion  or  rest ;  this  inability  is 
called  inertia.  Evidently  the  term  ought  never  to  be  employed 
to  denote  a  hindrance  to  motion  or  rest.  The  First  Law  of 
Motion  is  often  appropriately  called  the  Law  of  Inertia. 

IX.     SECOND  LAW  OF  MOTION,   AND  APPLICATIONS. 

If  a  person  wished  to  describe  to  }^ou  the  motion  of  a  ball 
struck  by  a  bat,  he  would  be  obliged  to  tell  you  three  things : 
(1)  where  it  started,  (2)  in  what  direction  it  moved,  and  (3)  how 
ri    70  far  it  went.    These  three  essential 

elements  may  be  represented  graphi- 
cally by  lines.  Thus,  suppose  balls 
at  A  and  D  (Fig.  70)  to  be  struck 
by  bats,  and  that  they  move  respec- 
tively to  B  and  E  in  one  second.  Then  the  points  A  and  D  are 
their  starting-points  ;  the  lines  A  B  and  D  E  represent  the  direc- 
tion of  their  motions,  and  the  lengths  of  the  lines  represent  both 
the  distances  traversed  and  the  relative  intensities  of  the  forces 
applied.  In  reading,  the  direction  should  be  indicated  by  the 
order  of  the  letters,  as  AB  and  DE. 

Let  a  force  whose  intensity  may  be  represented  numerically 
by  8  (e.g.,  8g),  acting  in  the  direction  AB  (Fig.  71),  be  applied 
continuously  to  a  ball  starting  at  A,  and  suppose  this  force  capa- 
ble of  moving  it  to  B  in  one  second  ;  now,  at  the  end  of  the  second 
let  a  force  of  the  intensity  4,  directed  at  right  angles  to  the  direc- 
tion of  the  former  force,  act  during  a  second,  —  it  would  move 
the  ball  to  C.  If,  however,  when  the  ball  is  at  A,  both  of  these 
forces  should  be  applied  at  the  same  time,  then  at  the  end  of  a 


COMPOSITION   OF  FORCES.  91 

second  the  ball  will  be  found  at  C.     Its  path  will  not  be  AB  nor 

AD,   but   an    intermediate    one, 

AC.    Still,  each  force  produces  in 

effect    its    own    separate    result, 

for  neither  alone  would  carry  it  to 

C,  but  both  are  required.    Hence, 

the 

§  69.  Second  law  of  motion. 

—  A  given  force  has  the  same  effect 

in  producing  motion,  whether  the 

body  on  which  it  acts  is  in  motion  or  at  rest;  whether  it  is  acted 

upon  by  that  force  alone,  or  by  others  at  the  same  time. 

§  70.  Composition  of  forces.  —  It  is  evident  that  a  single 
force,  applied  in  the  direction  AC  (Fig.  71),  might  produce  the 
same  result  that  is  produced  by  the  two  forces  AB  and  AD. 
Such  a  force  is  called  a  resultant.  A  resultant  is  a  single  force, 
that  may  be  substituted  for  two  or  more  forces,  and  produce  the 
same  result  that  the  combined  forces  produce.  The  several  forces 
that  contribute  to  produce  the  resultant  are  called  its  components. 
When  the  components  are  given,  and  the  resultant  required,  the 
problem  is  called  composition  of  forces.  The  resultant  of  two 
forces  acting  at  an  angle  to  each  other  is  always  a  diagonal  of  a 
parallelogram,  of  which  the  components  form  two  adjacent  sides. 
Thus,  the  lines  AD  and  AB  represent  respectively  the  direction 
and  relative  intensity  of  each  component,  and  AC  represents 
the  direction  and  intensity  of  the  resultant. 

The  numerical  value  of  the  resultant  may  be  found  by  com- 
paring the  length  of  the  line  A  C  with  the  length  of  either  A  B 
or  AD,  whose  numerical  values  are  known.  Thus,  AC  is  2.23 
times  AD  ;  hence,  the  numerical  value  of  the  resultant  AC  is 
4x  2.23  =  8.92. 

When  the  components  act  at  right  angles  to  each  other,  as  in 
Figure  71,  the  resultant  divides  the  parallelogram  into  two  equal 
right-angled  triangles  ;  and  the  intensity  of  the  resultant  may  be 


92  DYNAMICS. 

found  by  calculating  the  hypothenuse,  having  two  sides  of  either 
triangle  given.  Thus,  V42 -f-82=  8.9+  the  numerical  value  of 
the  resultant  AC. 

Copy  upon  paper  and  find  the  resultant  of  the  components 
AB  and  AC,  in  each  of  the  four  diagrams  in  Figure  72.     Also 

Fig.  72. 


assign  appropriate  numerical  values  to  each  component,  and  find 
the  corresponding  numerical  value  of  each  resultant. 

When  more  than  two  components  are  given,  find  the  resultant 
of  any  two  of  them,  then  of  this  resultant  and  a  third, 'and  so  on 
till  every  component  has  been  used.  Thus,  in  Figure  73,  AC  is 

the  resultant  of  AB  and  AD, 
and  AF  is  the  resultant  of  AC 
and  AE,  i.e.,  of  the  three  forces 
AB,  AD,  and  AE.  (Invent 
several  problems  similar  to  this, 
in  which  three,  four,  or  more 
forces  are  to  be  combined,  and 
work  out  the  results.) 

Generally  speaking,  a  motion 
may  be  the  result  of  any  number 
of  forces.  When  we  see  a  body  in  motion,  we  cannot  determine 
by  its  behavior  how  many  forces  have  concurred  to  produce  its 
motion. 

§  71.  Resolution  of  forces.  —  Assume  that  a  ball  moves  a 
certain  distance  in  a  certain  direction,  AC  (Fig.  74),  and  that 
one  of  the  forces  that  produces  this  motion  is  represented,  in 
intensity  and  direction,  by  the  line  AB;  what  must  be  the 


BESOLUTION  OF  FORCES.  93 

intensity  and  direction  of  the  other  force?  Since  AC  is  the 
resultant  of  two  forces  acting  at  an  angle  to  each  other  (§  70), 
it  is  the  diagonal  of  a  paral- 
lelogram of  which  AB  is  one 
of  the  sides.  From  C,  draw 
CD  parallel  and  equal  to 
BA,  and  complete  the  par- 
allelogram by  connecting 
the  points  B  and  C,  and  A 
and  D.  Then,  according  to  the  principle  of  composition  of 
forces,  AD  represents  the  intensit}'  and  direction  of  the  force 
which,  combined  with  the  force  AB,  would  move  the  ball  from 
A  to  C.  The  component  AB  being  given,  no  other  single  force 
than  AD  will  satisfy  the  question. 

Had  the  question  been,  What  forces  can  produce  the  motion 
AC?  an  infinite  number  of  answers  might  be  given.  In  a  like 
manner,  if  the  question  were,  What  numbers  added  together 
will  produce  50?  the  answer  might  be  20+30,  40  +  10,  20  + 
20  +  10,  and  so  on,  ad  Infinitum;  but  if  the  question  were, 
What  number  added  to  30  will  produce  50?  only  one  answer 
could  be  given. 

Experiment.  Verify  the  preceding  propositions  in  the  following 
manner :  From  pegs  A  and  B  Fi 

(Fig.  75),  in  the  frame  of  a 
blackboard,  suspend  a  known 
weight  W,  (say)  10  pounds,  by 
means  of  two  strings  con- 
nected at  C.  In  each  of  these 
strings  insert  dynamometers1 
x  and  y.  Trace  upon  the  black- 
board short  lines  along  the 
strings  from  the  point  C,  to 
indicate  the  direction  of  the 
two  component  forces ;  also 
trace  the  line  CD,  in  continuation  of  the  line  WC,  to  indicate  the 
direction  and  intensity  of  the  resultant.  Remove  jJie  dynamometers, 

1  Dynamometer,  force-measurer.    The  most  common  form  is  a  spring  balance. 


94  DYNAMICS. 

extend  the  lines  (as  Ca  and  C6),  and  on  these  construct  a  parallelogram, 
from  the  extremities  of  the  line  C  D  regarded  as  a  diagonal.  It  will 
be  found  that  10:  number  of  pounds  indicated  by  the  dynamometer 
x  : :  C  D :  Ca ;  also  that  10  :  number  of  pounds  indicated  by  the  dyna- 
mometer y  : :  CD:  Cb.  Again,  it  is  plain  that  a  single  force  of  10 
pounds  must  act  in  the  direction  C  D  to  produce  the  same  result  that  is 
produced  by  the  two  components.  Hence,  when  two  sides  of  a  parallelo- 
gram represent  the  intensity  and  direction  of  two  component  forces,  the 
diagonal  represents  the  resultant.  Vary  the  problem  by  suspending  the 
strings  from  different  points,  as  E  and  F,  A  and  F,  etc. 

§  72.  Composition  of  parallel  forces.  —  If  the  strings  CA 
and  CB  (Fig.  75)  are  brought  near  to  each  other,  as  when  sus- 
pended from  B  and  E,  so  that  the  angle  formed  by  them  is 
diminished,  the  component  forces,  as  indicated  by  the  dyna- 
mometers, will  decrease,  till  the  two  forces  become  parallel, 
when  the  sum  of  the  components  just  equals  the  weight  W. 
Hence,  (1)  two  or  more  forces  applied  to  a  body  act  to  the  greatest 
advantage  when  they  are  parallel,  and  in  the  same  direction,  in 
which  case  their  resultant  equals  their  sum. 

On  the  other  hand,  if  the  strings  are  separated  from  each 
other,  so  as  to  increase  the  angle  formed  by  them,  the  forces 
necessary  to  support  the  weight  increase  until  they  become  ex- 
actly opposite  each  other,  when  tbe  two  forces  neutralize  each 
other,  and  none  is  exerted  in  an  upward  direction  to  support  the 
weight.  If  the  two  strings  are  attached  to  opposite  sides  of  the 
weight  (the  weight  being  supported  by  a  third  string),  and 
pulled  with  equal  force,  the  weight  does  not  move.  But  if  one 
is  pulled  with  a  force  of  15  pounds,  and  tbe  other  with  a  force 
of  10  pounds,  the  weight  moves  in  the  direction  of  the  greater 
force  ;  and  if  a  third  dynamometer  is  attached  to  the  weight,  on 
the  side  of  the  weaker  force,  it  is  found  that  an  additional  force 
of  5  pounds  must  be  applied  to  prevent  motion.  Hence,  (2) 
when  two  or  more  forces  are  applied  to  a  body,  they  act  to  greater 
disadvantage  the  farther  their  directions  are  removed  from  one 
another;  and  the  result  of  parallel  forces  acting  in  opposite  direc- 
tions is  motion  in  the  direction  of  the  greater  force,  proportionate 
to  their  difference. 


COUPLE.  95 

When  parallel  forces  are  not  applied  at  the  same  point,  the 
question  arises,  What  will  be  the  point  of  application  of  their 
resultant  ?  To  the  opposite  extremities  of  a  bar  A  B  apply  two 
sets  of  weights,  which  Fig.  76. 

shall  be  to  each  other  as 
3:1.  The  resultant  is  a 
single  force,  applied  at 
some  point  between  A 
and  B.  To  find  this 
point  it  is  only  necessary 
to  find  a  point  where  a  single  force,  applied  in  an  opposite 
direction,  will  prevent  motion  resulting  from  the  parallel  forces  ; 
in  other  words,  to  find  a  point  where  a  support  may  be  applied 
so  that  the  whole  will  be  balanced.  That  point  is  found  by  trial 
to  be  at  the  point  C,  which  divides  the  bar  into  two  parts  so 
that  AC  :  CB  : :  1  :  3.  Hence,  (3)  when  two  parallel  forces  act 
upon  a  body  in  the  same  direction,  the  distances  of  their  points  of 
application  from  the  point  of  application  of  their  resultant  are 
inversely  as  their  intensities. 

The  dynamometer  E  indicates  that  a  force  equal  to  the  sum 
of  the  two  sets  of  weights  is  necessar}^  to  balance  the  two  forces. 
A  force  whose  effect  is  to  balance  the  effects  of  several  compo- 
nents is  called  an  equilibrant.  The  resultant  of  the  two  com- 
ponents is  a  single  force,  equal 
to  their  sum,  applied  at  C  in  the 
direction  CD. 


§  73.  Couple.  — If  two  equal, 
parallel,  and'  opposite  forces  are 
applied  to  opposite  extremities  of 
a  stick  AB  (Fig.  77),  no  single 
force  can  be  applied  so  as  to  keep  the  stick  from  moving ;  there 
will  be  no  motion  of  translation,  but  simply  a  rotation  around 
its  middle  point  C.  Such  a  pair  of  forces,  equal,  parallel,  and 
opposite,  is  called  a  couple. 


96  DYNAMICS. 

PROBLEMS,    ETC. 

1.  A  man  and  a  boy,  grasping  opposite  ends  of  a  pole  3m  long,  sup- 
port thereon  a  weight  of  50k  between  them.     Where  should  the  weight 
be  placed  that  the  boy  may  support  20k? 

2.  If  the  weight  were  placed  40cm  from  the  man,  how  much  would 
each  support? 

3.  Suppose  that  a  boat  is  headed  directly  across  a  river  half  a  mile 
wide,  and  is  rowed  with  a  velocity  that  would  land  it  upon  the  opposite 
shore  in  half  an  hour,  if  there  were  no  current;  but  the  current  carries 
the  boat  down  the  stream  at  the  rate  of  one  mile  an  hour.     Where  will 
the  boat  land? 

4.  How  far  will  it  travel? 

5.  How  long  will  it  be  in  crossing  the  river? 

6.  A  ship  is  sailing  due  south-east  at  the  rate  of  10  miles  per  hour, 
what  is  its  southerly  velocity  ? 

7.  Find,  both  by  construction  and  calculation,  the  intensity  of  two 
forces,  acting  at  right  angles  to  each  other,  that  will  support  a  weight 
of  15  pounds. 

8.  Verify  the  results  with  dynamometers. 


X.     OTHER  APPLICATIONS   OF  THE    SECOND   LAW  OF  MO- 
TION.—CENTER  OF  GRAVITY. 

Let  Figure  78  represent  any  body  of  matter ;  for  instance,  a 
stone.     Every  molecule  of  the  body  is  acted  upon  by  the  force 
Fi    78  of  gravity ;  tbe  intensity  of  this  force  is 

measured  by  the  weight  of  the  molecule. 
The  forces  of  gravity  of  all  the  molecules 
form  a  set  of  parallel  forces  acting  verti- 
cally downward,  the  resultant  of  which 
equals  their  sum,  and  has  the  same  direction 
as  its  components.  The  resultant  has  a 
definite  point  of  application  in  whatever 
«i  position  the  body  may  be,  and  this  point 

is  called  its  center  of  gravity.  The  center 
of  gravity  (e.g.)  of  a  body  is,  therefore,  the  point  of  application 
of  the  resultant  of  all  these  forces;  and  for  many  purposes  the 
whole  weight  of  the  body  may  be  supposed  to  be  concentrated  at 
its  center  of  gravity.  Hence  mathematicians,  by  the  place  of  a 
body,  usually  mean  that  point  where  the  c.  g.  is  situated. 


CENTER   OF   GRAVITY.  97 

Let  G  in  the  figure  represent  this  point.  For  many  practical 
purposes,  then,  we  may  consider  that  gravit}^  acts  only  upon  this 
point,  and  in  the  direction  GF.  If  the  stone  falls  freely,  this 
point  cannot,  in  obedience  to  the  first  law  of  motion,  deviate 
from  a  vertical  path,  however  much  the  body  may  rotate  during 
its  fall.  Inasmuch,  then,  as  the  e.g.  of  a  falling  body  always 
describes  a  definite  path,  a  line  GF  that  represents  this  path, 
or  the  path  in  which  a  body  supported  tends  to  move,  is  called 
the  line  of  direction. 

It  is  evident  that  if  a  force  equal  to  its  own  weight  and 
opposite  in  direction  is  applied  to  a  body  anywhere  in  the  line 
of  direction  (or  its  continuation),  this  force  will  be  the  equi- 
librant  of  the  forces  of  gravity ;  in  other  words,  the  body  sub- 
jected to  such  a  force  is  in  equilibrium,  and  is  said  to  be  sup- 
ported ^  and  the  equilibrant  is  called  its  supporting  force.  To 
support  any  body,  then,  it  is  only  necessary  to  provide  a  support 
for  its  center  of  gravity.  The  supporting  force  must  be  applied 
somewhere  in  the  line  of  direction,  otherwise  the  body  will  fall. 

Experiment.  —  Place  a  stick  of  wood,  two  meters  long,  horizontally 
across  the  tip  end  of  a  finger.  When  you  succeed  in  getting  the  finger 
directly  under  its  e.g.,  it  will  rest,  but  not  till  then.  The  difficulty  of 
poising  a  book,  or  any  other  object,  on  the  end  of  a  finger,  consists 
wholly  in  keeping  the  support  under  the  center  of  gravity. 

Figure  79  represents  a  toy  called  a  "witch,"  consisting  of  a 
cj'linder  of  pith  terminating  in  a  Fig  79 

hemisphere  of  lead.  The  toy  will  not 
lie  in  the  position  shown  in  the  figure 
on  a  horizontal  surface  «6,  because 
the  support  is  not  applied  immediately 
under  its  e.g.  at  G ;  but,  when  placed  horizontally,  it  immedi- 
ately assumes  a  vertical  position.  It  appears  to  the  observer 
to  rise  ;  but,  regarded  in  a  mechanical  sense,  it  really  falls,  be- 
cause its  e.g.,  where  all  the  weight  is  supposed  to  be  concen- 
trated, takes  a  lower  position. 


98  DYNAMICS. 

Whether  a  body  ivill  stand  or  fall  depends  upon  whether  or  not 
its  line  of  direction  falls  within  its  base.  The  base  of  a  body  is 
not  necessarily  limited  to  that  part  of  the  under  surface  of  a  body 
that  touches  its  support.  For  example,  place  a  string  around 
the  four  legs  of  a  table  close  to  the  floor :  the  rectangular  figure 
bounded  by  the  string  is  the  base  of  the  table.  (What  is  the 
base  of  a  man  when  standing  on  one  foot  ?  on  two  feet  ?) 

§  74.  How  to  find  the  center  of  gravity  of  a  body.  — 
Experiment.  Attach  a  string  to  a  potato  by  means  of  a  tack,  as  in 
Figure  80,  and  suspend  from  the  hand.  When  the  potato  comes  to  rest 
there  will  be  an  equilibrium  of  forces,  and 
the  e.g.  must  be  in  the  same  line  with  the 
equilibrant  of  gravity ;  hence,  if  a  knitting- 
needle  is  thrust  vertically  through  the  po- 
tato from  a,  so  as  to  represent  a  continua- 
tion of  the  vertical  line  oa,  the  e.g.  must 
lie  somewhere  in  the  path  an  made  by  the 
needle.  Suspend  the  potato  from  some 
other  point,  as  6,  and  a  needle  thrust  verti- 
cally through  the  potato  from  6  will  also 
pass  through  the  e.g.  Since  the  e.g.  lies 
in  both  the  lines  an  and  6s,  it  must  be  at  c, 
their  point  of  intersection.  It  will  be  found  that,  from  whatever  point 
the  potato  is  supported,  the  point  c  will  always  be  vertically  under  the 
point  of  support.  On  the  same  principle  the  e.g.  of  any  body  is  found. 
But  the  e.g.  of  a  body  may  not  be  coincident  with  any  particle  of  the 
body;  for  example,  the  e.g.  of  a  ring,  a  hollow  sphere,  etc. 

§  75.  Three  states  of  equilibrium.  —  The  weight  of  a 
body  is  a  force  tending  downward ;  hence,  a  body  tends  to  as- 
sume a  position  such  that  its  e.g.  will  be  as  low  as  possible. 

Experiment  1.  Try  to  support  a  ring  on  the  end  of  a  stick,  as  at 
b  (Fig.  81).  If  you  can  keep  the  support  exactly  under  the  e.g.  of  the 
ring,  there  will  be  an  equilibrium  of  forces,  and  the  ring  will  remain  at 
rest.  But  if  it  is  slightly  disturbed,  the  equilibrium  will  be  destroyed, 
and  the  ring  will  fall.  Support  it  at  a ;  in  this  position  its  e.g.  is  as 
low  as  possible,  and  any  disturbance  will  raise  its  e.g. ;  but,  in  conse- 


STABILITY   OF   BODIES.  99 

quence  of  the  tendency  of  the  e.g.  to  get  as  low  as  possible,  it  will 
quickly  fall  back  into  its  original  position. 

A  body  is  said  to  be  in  stable  equilibrium,  if  its  position  is 
such  that  a  disturbance  would  raise  its  _,. 

e.g.,  since  in  that  event  it  would  tend  to 
return  to  its  original  position.  On  the 
other  hand,  a  body  is  said  to  be  in  un- 
stable equilibrium  when  a  disturbance 
would  lower  its  e.g.,  since  it  would  not 
return  to  its  original  position. 

A  body  is  said  to  be  in  neutral  or  in- 
different equilibrium  when  it  rests  equally 
well  in  any  position  in  which  it  may  be 
placed.  A  sphere  of  uniform  density, 
resting  on  a  horizontal  plane,  is  in  neutral  equilibrium,  because 
its  e.g.  is  neither  raised  nor  lowered  by  a  change  of  base.  Like- 
wise, when  the  support  is  applied  at  the  e.g.,  as  when  a  wheel 
is  supported  by  an  axle,  the  body  is  in  neutral  equilibrium. 

It  is  evident  that,  if  the  e.g.  is  below  the  support,  as  in  the  last 
experiment  with  the  ring,  the  equilibrium  must  be  stable;  but,  as 
in  Figure  79,  a  body  may  be  in  stable  equilibrium,  though  its 
e.g.  is  above  the  point  of  support.  (When  is  this  possible?) 

It  is  difficult  to  balance  a  lead-pencil  on  the  end  of  a  finger ; 
but  by  attaching  two  knives  to  it,  as  in  Figure  82, 
the  e.g.  may  be  brought  below  the  support,  and  it 
may  then  be  rocked  to  and  fro  without  falling. 


§  76.  Stability  of  bodies.  —  The  ease  or  diffi- 
culty with  which  bodies  supported  at  their  bases  are 
overturned  depends  upon  the  hight  to  which  their 
e.g.  must  be  raised  in  overturning  them.  The  let- 
ter c  (Fig.  83)  marks  the  position  of  the  e.g.  of  each  of  the  four 
bodies  A,  B,  C,  and  D.  To  turn  any  one  of  these  bodies  over, 
its  e.g.  must  pass  through  the  arc  ci,  and  be  raised  through  the 
hight  ai.  By  comparing  A  with  B,  and  supposing  them  to  be 


100  DYNAMICS. 

of  equal  weight,  we  learn  that  of  two  bodies  of  equal  liiglit  and 
weight,  the  e.g.  of  that  body  which  has  the  larger  base  must  be 
raised  higher,  and  is,  therefore,  overturned  with  greater  difficulty. 
A  comparison  of  A  and  C,  supposing  them  to  be  of  equal 
weight,  shows  that  when  two  bodies  have  equal  bases  and  weights, 
the  higher  body  is  more  easily  overturned.  D  and  C  have  equal 
bases  and  hights,  but  D  is  made  heavy  at  the  bottom,  and  thi? 
lowers  its  e.g.  and  gives  it  greater  stability. 


Fig.  83. 


QUESTIONS. 

1.  Where  is  the  e.g.  of  a  box? 

2.  Why  is  a  pyramid  a  very  stable  structure  ? 

3.  What  is  the  object  of  ballast  in  a  vessel 't 

4.  State  several  ways  of  giving  stability  to  an  inkstand? 

5.  (a)  In  what  position  would  you  place  a  cone  on  a  horizontal 
plane,  that  it  may  be  in  stable  equilibrium  ?    (&)  That  it  may  be  in  neu- 
tral equilibrium  ?     (c)  That  it  may  be  in  unstable  equilibrium  ? 

6.  In  loading  a  wagon,  where  should  the  heavy  luggage  be  placed  ? 
Why? 

7.  Why  are  bipeds  slower  in  learning  to  walk  than  quadrupeds  ? 

8.  Why  is  mercury  placed  in  the  bulb  of  a  hydrometer  ? 

9.  How  will  a  man  rising  in  a  boat  affect  its  stability  ? 

10.  Which  is  more  liable  to  be  overturned,  a  load  of  hay  or  a  load  of 
stone  of  equal  weight  ? 

11.  (a)  How  would  you  place  a  book  upon  a  table,  that  it  may  be  in 
stable  equilibrium  ?     (6)  That  it  may  be  in  unstable  equilibrium? 


CURVILINEAR   MOTION.  >  ^  ,  ,  ,       101 


XI.       OTHER    APPLICATIONS    OF    THE     SECONlV   LAW    (tf 
MOTION.  —  CURVILINEAR    MOTION. 

According  to  the  first  law  of  motion,  every  moving  body  pro- 
ceeds in  a  straight  line,  unless  compelled  to  depart  from  it  by 
some  external  force.  If  the  external  force  is  continuous,  i.e., 
acts  at  every  point,  the  direction  is  changed  at  every  point,  and 
the  result  is  a  curvilinear  motion;  and  if  the  force  is  constant, 
and  acts  at  right  angles  to  the  path,  the  curve  becomes  a  circle. 

Thus,  suppose  a  ball  at  A  (Fig.  84) ,  suspended  by  a  string  from  a 
point  d,  to  be  struck  by  a  bat,  in  a  manner  that  would  cause  it  to  move 
in  the  direction  Ao. 

path  by  the  tension  of  the  string,  which 
operates  like  a  force  drawing  it  toward  Fig.  si. 

d.  It  therefore  takes,  in  obedience  to 
the  two  forces,  an  intermediate  course 
toward  c.  At  c  its  motion  is  in  the  di- 
rection en,  in  which  path  it  would  move, 
but  for  the  string,  in  accordance  with 
the  first  law  of  motion.  Here,  again,  it 
is  compelled  to  take  an  intermediate 
path  toward  e.  Thus,  at  every  point, 
the  tendency  of  the  moving  body  is  to 
preserve  the  direction  it  has  at  that 
point,  and  consequently  to  move  in  a 
straight  line.  The  only  reason  it  does 

not  so  move,  is  that  it  is  at  every  point  forced -from  its  natural  path 
by  the  pull  of  the  string.  But  if,  when  the  ball  reaches  the  point  z, 
the  string  is  cut,  the  ball,  having  no  force  operating  to  change  its  mo- 
tion, continues  in  the  direction  in  which  it  is  moving  at  that  point; 
i.e.,  in  the  direction  ih,  which  is  a  tangent  to  its  former  circular  path. 

This  tendency  of  a  body  moving  in  a  curvilinear  path  to  fly 
off  in  a  straight  line  has  been  erroneously  attributed  to  a  sup- 
posed "centrifugal  force,"  which  is  constantly  urging  it  away 
from  the  center,  its  escape  being  prevented  only  by  a  force 
pulling  it  toward  the  center. 

Centrifugal  force  has  in  reality  no  existence ;  the  results  that 


102      c  c  .  tc  t    :  DYNAMICS. 


,  ^re  commonly  attributed  to  it  are  due  entirely  to  the  tendency 
'of  inoviug  bodies'  to  move  in  straight  lines  in  consequence  of 
their  inertia.  If  a  moving  bodj7  is  to  describe  a  curvilinear 
path,  a  force  called  a  centripetal  force  must  be  constantly  applied 
to  it  at  an  angle  to  its  otherwise  straight  path.  [We  shall  make 
use  of  the  expression  centrifugal  force  for  want  of  a  better  one, 
and  because  it  has  obtained  universal  curremry.] 

The  greater  the  velocity  of  the  moving  body,  the  greater  must 
be  the  force  applied  to  produce  a  given  departure  from  a  straight 
line.  This  may  be-  shown  by  suspending  a  weight  to  a  dyna- 
mometer, and  swinging  them  about  the  hand.  If,  when  30 
revolutions  are  made  in  a  minute,  the  force,  as  indicated  by  the 
dynamometer,  is  4  pounds,  then,  on  doubling  its  velocity,  the 
force  will  be  increased  to  16  pounds.  If  the  weight  is  doubled 
and  the  velocity  remains  the  same,  this  force  will  be  doubled. 
Hence,  to  produce  circular  motion,  the  centripetal  force  must  be 
increased  as  the  square  of  the  velocity  increases,  and  as  the  mass 
increases. 

The  farther  a  point  is  from  the  axis  of  motion,1  the  farther  it 
has  to  move  during  a  rotation,  consequently  the  greater  its 
velocity.  Hence,  bodies  situated  at  the  earth's  equator  have 
the  greatest  velocity,  due  to  the  earth's  rotation,  and  consequently 
the  greatest  tendency  to  fly  off  from  the  surface,  the  effect  of 
which  is  to  neutralize,  in  some  measure,  the  force  of  gravity.  It 
is  calculated  that  a  body  weighs  about  ^^-g-  less  at  the  equator  than 
at  either  pole,  in  consequence  of  the  greater  centrifugal  force  at 
the  former  place.  But  289  is  the  square  of  17;  hence,  if  the 
earth's  velocity  were  increased  seventeen-fold,  objects  at  the 
equator  would  weigh  nothing. 

We  have  also  learned  (page  22)  that  a  body  weighs  more  at 
the  poles  in  consequence  of  the  oblateness  of  the  earth.  This 
is  estimated  to  make  a  difference  of  about  -5--^.  Hence,  a  body 
will  weigh  at  the  equator  about  ^^  -f  -^  —  T-|^¥  less  than  at  the 
poles. 

1  Axis,  an  imaginary  straight  line  passing  through  a  body  about  which  it  rotates. 


QUESTIONS. 


103 


Experiment.  Arrange  some  kind  of  rotating  apparatus,  e.g.,  A, 
Figure  85.  Suspend  a  skein  of  thread  a  by  a  string,  and  rotate ;  it 
assumes  the  shape  of  the  oblate  spheroid  a'.  This  illustrates  the 
probable  method  by  which  the  earth,  on  the  supposition  that  it  was 
once  in  a  fluid  state,  assumed  its  present  spheroidal  state.  (Explain.) 
Suspend  a  glass  fish  aquarium  e,  about  one-tenth  full  of  colored  water, 
and  rotate.  The  liquid  gradually  leaves  the  bottom,  rises,  and  forms  an 


QJ 


equatorial  ring  within  the  glass.  Pass  a  string  through  the  longest 
diameter  of  an  onion  c,  and  rotate;  the  onion  gradually  changes  its 
position  so  as  to  rotate  on  its  shortest  axis.  (Explain.)  A  chain  6  as» 
sumes  on  rotation  a  similar  position. 


QUESTIONS. 

1.  Why  does  not  the  sphere  d  (Fig.  85)  change  its  position  when 
rotated? 

2.  Why  does  the  earth  rotate  on  its  shortest  axis? 

3.  State  the  various  facts  illustrated  in  the  act  of  slinging  a  stone. 

4.  (a)  When  will  water  and  mud  fly  off  from  the  surface  of  a  rev 
volving  wheel?    (&)  Why  do  they  fly  off?     (c)  In  what  direction  do 
they  fly  ? 

5.  What  is  the  force  that  keeps  the  earth  and  the  other  planets  in 
their  orbits? 

6.  How  do  you  account  for  their  curvilinear  motion? 


104  DYNAMICS. 


XII.     OTHER  APPLICATIONS   OF  THE   SECOND  LAW  OF 
MOTION. —ACCELERATED   AND   RETARDED   MOTION. 

§  77.  Accelerated  motion  or  velocity.  —  So  far  the  only 
case  of  motion  under  the  action  of  a  continuous  force  that  we 
have  studied  is  that  of  curvilinear  motion,  in  which  the  force 
acts  at  an  angle  to  the  direction  of  the  motion  at  every  point, 
and  so  the  direction  of  the  force  is  constantly  changing ;  but  if 
the  motion  takes  place  in  the  same  straight  line  as  that  in  which 
the  force  acts,  we  shall  have  one  of  the  cases  of  varied  motion 
referred  to  on  page  87. 

Even  if  several  men  push  against  a  heavy  car  we  may  be  un- 
able to  recognize  any  motion  for  two  or  three  seconds ;  but,  if 
they  continue  to  exert  force  upon  the  car,  it  will  move  with 
greater  and  greater  velocity  until  the  resisting  force  (which  in- 
creases with  the  velocity) -becomes  equal  to  that  applied  by  the 
men.  This  continually  increasing  velocity  is  termed  acceler- 
ated velocity. 

The  most  familiar  illustration  is  that  of  falling  bodies.  We 
are  sufficiently  aware  of  the  difference  in  the  results  that  would 
follow  a  jump  from  a  fifth-story  window  and  a  jump  from  a 
first-story  window.  Inasmuch  as  the  velocity  of  falling  bodies 
is  so  great  that  there  is  not  time  for  accurate  observation  during 
their  fall,  we  must  resort  to  some  method  of  checking  their 
velocity,  without  otherwise  changing  the  character  of  the  fall. 

Experiment.    Take  a  smooth  board  (Fig.  86),  about  4m  long,  and 
place  it  so  that  one  end  shall  be  about  4cm  higher  than  the  other.     Sus- 
pend within  easy  view 
Figt  86'  a  string  (about  lm  long) 


and  ball,  as  a  pendu- 
lum. Set  it  in  vibra- 
tion, and,  at  the  instant 
the  ball  reaches  one  extremity  of  its  arc,  let  a  marble  begin  to  roll 
down  the  inclined  plane.  Let  another  person  mark  the  point  on  the 
board  that  the  ball  reaches  at  the  end  of  one  swing  of  the  pendulum. 
Repeat  the  operation  several  times,  and  mark  the  points  that  it  reaches 


ACCELERATED   MOTION   OR   VELOCITY. 


105 


at  the  end  of  the  second  and  third  swings ;  also  verify  the  preceding 
points  by  several  trials;  if  there  is  a  difference,  take  the  mean  dis- 
tance between  the  points  obtained  at  the  end  of  a  given  swing  for  an 
approximate  result.  If  the  experiment  is  conducted  with  care,  it  will 
be  found  that  during  the  first  swing,  which  we  call  a  unit  of  time  (T), 
the  marble  moves  through  a  certain  space,  which  we  represent  by  the 
expression  |  k ;  during  the  second  unit  of  time  it  moves  through  f  k, 
three  times  the  space  that  it  did  in  the  first  unit  of  time ;  and  during 
the  third  unit  of  time  it  moves  through  |  k. 

Arrange  the  results  of  your  observations  in  a  tabulated  form  as  fol- 
lows: — 


No.  of  units  of 
time. 

Total  distance 
passed  over. 

Distance  passed 
over    in    each 
unit;  also  av- 
erage velocity. 

Increase  of  ve- 
locity in  each 
unit,  i.e.,  ac- 
celeration. 

Velocity  at  the 
end    of    each 
unit. 

1 

i(HO 

*'«!*) 

Hi*) 

2(1*) 

2 

4     " 

3     " 

2     " 

4     " 

3 

9     " 

5     " 

2     " 

6     " 

4 

16     " 

7     " 

2     " 

8     " 

etc. 

etc. 

etc. 

etc. 

etc. 

The  marble,  under  the  influence  of  gravity,  starts  from  a 
state  of  rest,  and  moves  through  one  space  in  a  unit  of  time. 
Gravity,  continuing  to  act,  accomplishes  no  more  nor  less  dur- 
ing any  subsequent  unit  of  time.  But  the  marble  moves  through 
three  spaces  during  the  second  unit ;  hence,  two  of  the  spaces 
must  be  due  to  the  motion  it  had  acquired  during  the  first  unit. 
In  other  words,  if  the  action  of  gravity  were  suspended  at  the 
end  of  the  first  unit,  the  marble  would  still  move  on,  and  would 
pass  through  two  spaces  during  the  second  unit.  It  therefore 
has  at  the  end  of  the  first  unit  a  velocity  (V)  of  two  spaces  (k) . 
But  it  started  from  a  state  of  rest ;  hence  the  constant  action  of 
gravity  causes,  during  the  first  unit,  an  acceleration  of  velocity 
equal  to  two  spaces  (k) ;  and  it  causes  the  same  acceleration 
during  every  subsequent  unit.  The  distance  k  is  called  the  ac- 
celeration due  to  the  constant  force.  A  body  impelled  by  a  single 
constant  force,  and  encountering  no  resistances,  always  has  a 
uniformly  accelerated  motion. 


106  DYNAMICS. 

§  78.  Formulas  for  uniformly  accelerated  motion.  - 
If  we  represent  the  distance  traversed  during  a  given  unit  of 
time  by  s,  and  the  total  distance  the  body  has  accomplished 
from  the  outset  to  the  end  of  a  given  unit  of  time  by  S,  we  have 
the  following  formulas  for  solving  problems  of  uniformly  accel- 
erated motion  •  — 

(1)  V=(£fcx2T)  =  &T. 

(2)  «=J*(2T-1). 

(3)  B  =  **T*>  or8  =  tfT*.  (See  §79.) 


§  79.  Velocity  of  a  falling  body  independent  of  its 
mass  and  kind  of  matter.  —  If  we  grasp  a  coin  and  a  feather 
between  the  thumb  and  finger,  and  release  both  at  the  same  in- 
stant, the  coin  will  reach  the  floor  first.  It  would  seem  as 
though  a  heavy  body  falls  faster  than  a  light  body.  Galileo  was 
the  first  to  show  the  falsity  of  this  assumption.  He  let  drop 
from  an  eminence  iron  balls  of  different  weights  :  they  all 
reached  the  ground  at  the  same  instant.  Hence  he  concluded, 
that  the  velocity  of  a  falling  body  is  independent  of  its  mass.  (This 
celebrated  experiment  should  be  repeated  by  every  student.) 

He  also  dropped  balls  of  wax  with  the  iron  balls.  The  iron 
balls  reached  the  ground  first.  Are  some  kinds  of  matter  affected 
Fig.  87  more  strongly  by  gravitation  than  others  ?  If  a  coin  and  a 
feather  are  placed  in  a  long  glass  tube  (Fig.  87),  and  the 
air  exhausted,  and  the  tube  turned  end  for  end,  it  wili 
be  found  that  the  coin  and  the  feather  will  fall  with  equal 
velocities.  Hence,  gravity  attracts  all  matter  alike;  but, 
inasmuch  as  a  wax  ball  presents,  according  to  the  amount 
of  matter  in  each,  more  surface  for  resistance  of  the  air 
than  an  iron  ball,  it  falls  more  slowly.  We  conclude, 
therefore,  that  all  bodies  fall  with  equal  velocities  in  a 
vacuum. 

When  the  bod}T  falls  freely,  and  the  unit  of  time  is  one 
second,  we  use  the  letter  g  instead  of  k  to  represent  the 
acceleration.     Experiments  show  that  in  the  latitude  of 
all  the  Northern  States  the  value  of  g  is  9.8m,  or  about 
32J  ft.  ;  that  is,  the  velocity  gained  if  the  force  of  gravity  acts 


RETARDED  MOTION.  107 

one  second  is  9.8m  per  second,  and  the  body  would  fall  in  the 
first  second  4.9'n  or  16^  ft. 

§  80.  Retarded  Motion.  —  If  we  reverse  the  order  of  the 
figures  in  Figure  86,  the  same  diagram  will  represent  the  motion 
of  a  body  rolling  upward,  or  the  motion  of  a  body  under  the  influ- 
ence of  a  retarding  force.  The  formulas  given  (§78)  for  find- 
ing velocities,  etc.,  of  bodies  having  uniformly  accelerated 
motion,  may  be  used  for  finding  velocities,  etc.,  of  bodies  having 
uniformly  retarded  motion ;  but  the  questions  should  be  so 
framed  as  to  be  an  exact  converse  of  the  questions  to  be  solved. 
Thus,  if  we  would  find  the  velocity  of  a  body  at  the  end  of  the 
first  second,  or  at  the  beginning  of  the  second  second,  thrown 
upward  by  a  force  that  would  cause  it  to  rise  six  seconds,  we 
should  calculate  the  velocity  that  a  falling  body  has  at  the  end 
of  the  fifth  second,  or  at  the  beginning  of  the  sixth  second. 

PROBLEMS. 

(Solve  these  problems  in  both  the  metric  and  the  English  measures.) 

1.  Disregarding  the  resistance  of  the  air,  what  distance  will  a  body 
fall  from  a  state  of  rest  in  five  seconds?  lftX,«v"*-  H*  *»*•  r*  fcr*»      )  3  v 

2.  What  distance  will  it  fall  during  the  fifth  second?  4-</--f  *~" 

3.  What  is  its  velocity  at  the  end  of  the  fifth  second?  ^."SJXoST 

4.  A  stone,  dropped  from  a  balloon,  strikes  the  ground  in  seven 
seconds.     How  high  is  the  balloon?  **>•»  "***-t  U  fc  j* 

5.  Under  the  influence  of  a  constant  force,  a  body  moves  500m  in  a 
impute.     How  far  will  it  go  in  an  hour? 

6.  What  will  be  its  velocity  at  the  end  of  the  first  half -hour? 

7.  How  far  will  it  move  during  the  fifty-ninth  minute? 

8.  A  body  falls  four  seconds ;  meantime  it  is  acted  on  by  a  constant 
force  which  causes  it  to  move  in  a  horizontal  direction  2m  in  the 
first  second.     Where  will  it  strike  the  ground? 

9.  What  is  its  horizontal  velocity  at  the  end  of  the  fourth  second? 

10.  What  is  its  vertical  velocity  at  the  end  of  the  fourth  second? 

11.  With  what  vertical  velocity  must  a  body  start  that  it  may  ascend 
three  seconds? 

12.  How  far  does  it  rise  during  the  first  second? 

13.  At  what  point  does  a  ball  shot  horizontally  from  a  gun  begin  to 
fall? 


108  DYNAMICS. 

§  81.  Projectiles.  —  Experiment.  Take  a  bottomless  tin  can 
A  (Fig.  88),  and  connect  a  rubber  tube  C,  2m  long,  with  a  glass  tube 
passing  through  a  stopper  at  B,  and  insert  a  short  glass  tube  at  D. 
Keep  the  can  filled  with  water,  bend  the  lower  part  of  the  rubber  tube 
at  D,  so  as  to  direct  the  stream  at  different  angles  of  elevation,  and 
observe  the  peculiarities  of  the  curves  formed  by  the  streams,  and  the 
different  vertical  and  horizontal  distances  reached  by  each". 

In  this  experiment  you  have  a  miniature  representation  of  the 
paths  of  all  projectiles,1  such  as  cannon-balls,  stones  thrown 
from  the  hand,  etc.  The  horizontal  distance  that  the  projectile 
attains  is  called  its  range  or  random.  Theoretically,  the  great- 
est range  is  obtained  at  an  angle  of  45° ;  but  practically,  on 
account  of  the  resistance  of  the  air,  it  is  at  a  little  less  thau  40°. 

Fig.  88. 


Every  projectile  is  acted  upon  by  two  forces :  (1)  the  force  of 
gravity,  and  (2)  the  resistance  of  the  air.  It  also  has  a  certain 
velocity  and  direction  at  the  instant  of  projection.  If  this 
velocity  and  direction  are  known,  and  the  resistance  of  the  air  is 
disregarded,  the  path  of  a  projectile  can  be  determined.  Thus, 
suppose  that  a  projectile  is  thrown  from  A  (Fig.  89)  at  an 

* Projectile,  a  body  thrown. 


PEOJECTILES.  109 

angle  of  45°,  that  it  is  in  the  air  six  units  of  time,  and  that  the 
vertical  hights  reached  at  the  end  of  the  first  three  units  succes- 
sively, are  B,  C,  and  D.  Its  horizontal  motion,  if  unimpeded, 
is  uniform,  and  the  corresponding  points  reached  in  that  direc- 
tion at  the  same  moments  are  (say)  B',  C',  and  D'.  Combining 
these  two  motions, we  obtain  the  points  B",  C",  and  D",  reached 
by  the  projectile  successively,  at  the  end  of  each  of  the  first  three 
units  of  time.  The  force  of  gravity  constantly  acting  to  change 
its  direction,  it  must  describe,  during  the  first  three  units,  the 
curved  line  AB"C"D'f.  Since  the  time  of  ascent  and  descent 
are  equal,  it  must  reach  its  greatest  vertical  hight  at  the  end  of 
the  third  unit,  when  it  begins  its  descent.  The  path  of  descent 
D"E"F"G"  is  found  in  a  similar  manner.  The  path  thus  de- 
scribed is  known  as  a  parabolic  curve ;  but,  inasmuch  as  this  is 
practically  modified  by  the  resistance  of  the  air,  it  in  reality 
describes  a  peculiar  path  called  a  ballistic  curve.  The  curve 

Fig.   89. 


D"E"F"G"  represents  also  the  path  of  a  projectile  thrown  from 
D",  in  the  direction  of  the  line  D"G',  with  a  horizontal  velocity 
that  it  would  cause  it  to  reach  G'  at  the  end  of  the  third  unit  of 
time. 

An  excellent  verification  of  the  second  law  of  motion  is  found 
in  the  fact  that  a  ball,  projected  horizontally,  will  reach  the 
ground  in  precisely  the  same  time  that  it  would  if  dropped  from 
a  state  of  rest  from  the  same  hight.  That  is,  any  previous 
motion  a  body  has  in  any  direction  does  not  affect  the  action 
of  gravity  upon  the  body. 


no 


DYNAMICS. 


Experiment  2.  Support  two  iron  bars,  a  and  b  (Fig.  90),  bent  into 
the  form  of  a  curve,  about  3cm  apart,  and  so  situated  that  a  ball  n,  roll- 
ing down  them,  will  be  discharged  from  them  iu  a  horizontal  direction. 
So  connect  the  wires  of  an  electric  battery  c  with  these  bars,  that  while 
the  iron  ball  n  rests  upon  them  the  circuit  is  closed,  and  the  iron  ball 
m  is  supported  by  the  attraction  of  the  electro-magnet  e.  Now  allow 
n  to  roll  down  the  curved  path.  When  it  leaves  the  bars,  the  circuit  is 
broken,  e  instantly  loses  its  power  to  hold  m,  and  m  drops.  But  both 
balls  reach  the  floor  at  the  same  instant.  If  the  horizontal  velocity  of 
n  is  varied,  by  allowing  it  to  start  at  different  points  on  the  bars,  so  a? 
to  cause  it  to  describe  different  paths,  the  two  balls  will,  in  every  case 
acquire  exactly  equal  vertical  velocities. 

Fig.  90. 


XIII.     OTHER   APPLICATIONS    OF   THE   SECOND   LAW   OF 
MOTION.  —  THE   PENDULUM. 

Experiment  1.  From  a  bracket  suspend  by  strings  leaden  balls,  as 
in  Figure  91.  Draw  B  and  C  one  side,  and  to  different  hights,  so  that 
B  may  swing  through  a  short  arc,  and  let  both  drop  at  the  same  instant. 
C  moves  much  faster  than  B,  and  completes  a  longer  journey  at  each 
swing,  but  both  complete  their  swing,  or  vibration,  in  the  same  time. 

Hence,  (1)  the  time  occupied  by  the  vibration  of  a  pendulum 
is  independent  of  the  length  of  the  arc.  Of  only  very  small  arcs 


CENTER   OF  OSCILLATION.  Ill 

may  this  law  be  regarded  as  practically  true.  The  pendulum 
requires  a  somewhat  longer  time  for  a  long  arc  of  vibration  than 
for  a  short  one,  but  the  difference  becomes  perceptible  only  when 
the  difference  between  the  arcs  is  great,  and  then  only  after  many 
vibrations. 

Experiment  2.  Set  all  the  balls  swinging ;  only  B  and  C  swing  to- 
gether ;  the  shorter  the  pendulum,  the  Fig  9L 
faster  it  swings.  Make  B  lm  long,  and 
F  £m  long.  "Watch  in  hand,  count  the 
vibrations  made  by  B%  It  completes 
just  60  vibrations  in  a  minute ;  in  other 
words,  it  "  beats  seconds."  A  pendu- 
lum, therefore,  to  beat  seconds  must 
be  lm  long  (more  accurately,  .993m,  or 
39.09  in.).  Count  the  vibrations  of 
F ;  it  makes  120  vibrations  in  the  same 
time  that  B  makes  60  vibrations.  Make 
G  one-ninth  the  length  of  B ;  the  for- 
mer makes  three  vibrations  while  the 
latter  makes  one,  consequently  the 
time  of  vibration  of  the  former  is  one- 
third  that  of  the  latter. 

Hence,  (2)  the  time  of  one  vibra- 
tion of  a  pendulum  varies  as  the 
square  root  of  its  length. 

QUESTIONS  AND  PROBLEMS. 

1.  What  would  be  the  effect  if  B  were  made  twice  as  heavy  as  C? 
Why? 

2.  What  is  the  length  of  a  pendulum  that  beats  half-seconds?    Quar- 
ter-seconds?   That  makes  one  vibration  in  two  seconds?    That  makes 
two  vibrations  per  minute? 

3.  State  the  proportion  that  will  give  the  number  of  vibrations  per 
minute  made  by  a  pendulum  40*™  long. 

§  82.  Center  of  oscillation.  —  Experiment  1.  Connect  six 
balls,  at  intervals  of  15cm,  by  passing  a  wire  through  them,  after  the 
manner  of  pendulum  A.  This  forms  a  compound  pendulum  composed 


112  DYNAMICS. 

of  six  simple  pendulums.  Set  A  and  B  vibrating;  A  vibrates  faster 
than  B,  although  their  lengths  are  the  same.  Why  is  this?  If  A  were 
actuated  only  by  the  ball  /,  it  would  vibrate  in  unison  with  B.  If  the 
ball  a  were  free,  it  would  move  much  faster  than  /;  but,  as  they  are 
constrained  to  move  together,  the  tendency  of  a  is  to  quicken  the 
motion  of  /,  and  the  tendency  of  /  is  to  check  the  motion  of  a.  But  e 
is  quickened  less  than  /,  and  d  less  than  e;  on  the  other  hand,  b  is 
checked  by  /  less  than  «,  and  c  less  than  6.  It  is  apparent  that  there 
must  be  some  point  between  a  and  /,  whose  velocity  is  neither  quick- 
ened nor  checked  by  the  combined  action  of  the  balls  above  and  below 
it,  and  where,  if  a  single  ball  were  placed,  it  would  make  the  same 
number  of  vibrations  in  a  given  time  that  the  compound  pendulum 
does.  Shorten  pendulum  B,  and  find  the  required  point.  This  point 
is  called  the  center  of  oscillation. 

Every  compound  pendulum  is  equivalent  to  a  simple  pendulum, 
whose  length  is  equal  to  the  distance  between  the  center  of  oscilla- 
tion and  the  point  of  suspension  of  the  compound  pendulum.  In- 
asmuch as  the  distance  between  the  point  of  suspension  and  the 
center  of  oscillation  determines  the  rate  of  vibration,  whenever 
the  expression  length  of  pendulum  is  used,  it  must  be  understood 
to  mean  this  distance.  Strictly  speaking,  a  simple  pendulum  is 
a  heavy  material  point  suspended  by  a  weightless  thread.  Of 
course  such  a  pendulum  cannot  actually  exist ;  but  the  leaden 

kail,  suspended  by  a  thread,  is  a  near   approximation 

to  it. 

Experiment  2.  Suspend  on  the  frame  of  Figure  91  a  lath 
AB  (Fig.  92),  lm  long,  and  shorten  the  pendulum  B  till 
it  swings  in  the  same  period  as  the  lath ;  the  ball  of  B 
marks  the  center  of  oscillation  of  the  lath,  which  is  found 
to  be  two-thirds  the  length  of  the  lath  below  the  point 
of  suspension.  Attach  a  pound-weight  to  the  lower  end  of 
AB ;  its  vibrations  are  now  slower,  and  the  simple  pendulum 
B  must  be  lengthened  to  vibrate  in  the  same  time  as  the  lath 
and  weight;  hence  the  center  of  oscillation  of  the  lath  is 
lowered  by  the  addition  of  the  weight.  Move  the  weight 

up  the  lath;  the  vibrations  are  quickened.     (What  is  the  office  of  a 

pendulum  bob?) 

Experiment  3.  Remove  the  weight,  bore  a  hole  through  the  lath  at 


CENTER  OF  PERCUSSION.  113 

its  center  of  oscillation  C,  and,  passing  a  knitting-needle  through  the 
hole,  invert  the  lath  and  suspend  it  by  the  needle.  The  pendulum  is 
now  apparently  shortened,  and  we  naturally  expect  that  its  vibrations 
will  be  quicker  than  when  suspended  from  A.  But  the  part  B  C  now 
vibrates  in  opposition  to  the  part  C  A,  rising  as  it  sinks,  and  sinking  as 
it  rises.  This  tends  to  check  the  rapidity  of  the  vibrations  of  CA, 
and  it  is  found  that  the  pendulum  vibrates  in  the  same  time  when  sus- 
pended from  C  as  when  suspended  from  A. 

The  point  of  suspension  and  the  center  of  oscillation  are  inter- 
changeable; in  other  words,  there  are  always  two  points  in  a  com- 
pound pendulum  about  which  it  will  oscillate  in  the  same  time. 

This  suggests  a  practical  way  of  finding  the  center  of  oscilla- 
tion, and  the  equivalent  length  of  a  compound  pendulum.  For 
we  have  only  to  find  another  point  of  suspension  from  which  the 
pendulum  makes  the 
same  number  of  vibra- 
tions, in  a  given  time, 
as  from  its  usual  point 
of  suspension :  that 
point  is  its  center  of 
oscillation ;  and  the 
distance  between  it  and 
the  usual  point  of  sus- 
pension is,  technically 
speaking,  the  length  of 
the  pendulum.  It  will 
be  seen  that  these  two  points  are  unequally  distant  from  the 
center  of  gravity. 

§  83.  Center  of  percussion.  —  Experiment.  Suspend  the 
lath  by  a  string  attached  to  one  of  its  extremities,  and  with  a  club 
strike  it  horizontally  near  its  upper  extremity.  This  end  of  the  lath 
moves  in  the  direction  of  the  stroke  (A,  Fig.  93),  at  the  same  time 
causing  a  sudden  jerk  on  the  string,  which  is  felt  by  the  hand.  Strike 
the  lath  in  the  same  direction,  near  its  lower  extremity ;  the  upper  end 
of  the  lath  now  moves  in  a  direction  opposite  to  the  stroke  (B),  at  the 
same  time  causing  a  similar  jerk  of  the  string.  Next  strike  the  lath 


114  DYNAMICS. 

successively  at  points  higher  and  higher  above  its  lower  extremity ;  it 
is  found  that  the  jerk  on  the  string  becomes  less  till  the  center  of  oscil- 
lation is  reached,  when  no  pull  on  the  string  is  felt,  and  neither  end 
of  the  lath  tends  to  precede  the  other,  but  both  move  on  together  (C). 
The  full  force  of  the  blow  is  spent  in  moving  the  stick,  and  none  is 
expended  in  pulling  the  string.  This  point  is  called  the  center  of  per- 
cussion. 

The  center  of  percussion  is  coincident  with  the  center  of  oscilla- 
tion. It  is  the  point  where  a  blow,  given  or  received,  is  most 
effective,  and  produces  the  least  strain  upon  the  support  or  axis 
of  motion.  The  base-ball  player  soon  learns  at  what  point  on 
his  bat  he  can  deal  the  most  effective  blow  to  the  ball,  and  at 
tbe  same  time  feel  the  least  tingle  in  his  hands. 

§  84.  Some  useful  applications  of  the  pendulum.  — 
The  force  that  keeps  a  pendulum  vibrating  is  gravity.  Were 
it  not  for  friction  and  resistance  of  tbe  air,  a  pendulum,  once 
set  in  motion,  would  never  cease  vibrating.  Since  the  force 
of  gravity  keeps  the  pendulum  in  motion,  it  follows  that  the  rate 
of  vibration  of  a  given  pendulum  must  be  determined  by  the 
intensity  of  this  force.  Hence  it  is  apparent,  that  if  the  rate 
of  vibration  is  known,  the  intensity  of  the  force  of  gravity  may 
be  calculated.  It  is  found  by  experiment  that  the  time  of  vi- 
bration varies  inversely  as  the  square  root  of  the  force  of  gravity. 

So  the  pendulum  becomes  a  most  serviceable  instrument  for 
measuring  the  inteiisit}^  of  gravity  at  various  altitudes  and  at 
different  latitudes  on  the  earth's  surface.  (Compare  §  21).  It 
is  also  the  most  accurate  instrument  for  measuring  time  that  has 
been  invented.  Its  value,  as  a  time-measurer,  depends  upon 
the  absolute  uniformity  of  the  rate  of  vibration  as  long  as  its 
length  is  constant,  and  the  length  of  its  arc  very  small.  But  as 
heat  is  ever  modifying  the  dimensions  of  all  visible  bodies, 
various  devices  have  been  called  into  existence  by  which  heat 
may  be  made  to  correct  automatically  its  own  mischief.  Clocks 
that  do  not  have  self -regulating  pendulums  are  fast  in  winter 
and  slow  in  summer.  (How  would  you  regulate  them  ?) 


MOMENTUM.  115 

• 

QUESTIONS. 

1.  Where  is  the  center  of  percussion  iii  a  hammer  or  axe  ?    Why  ? 

2.  At  what  point  (disregarding  the  length  aucl  weight  of  the  arm 
that  swings  it)  should  a  blow  be  dealt  with  a  bat  of  uniform  dimen- 
sions when  held  in  the  hand  at  one  extremity  ? 

3.  What  change  in  the  location  of  the  center  of  percussion  is  pro- 
duced by  making  one  end  of  a  bat  heavier  than  the  other  ? 

4.  Which  end  of  a  bat,  the  heavier  or  lighter,  should  be  held  in  the 
hands  ?    Why  ? 

XIV.     MOMENTUM.  —  THIRD  LAW   OF  MOTION. 

§  85.  Momentum.  —  A  small  stone  dropped  upon  a  cake  of 
ice  produces  little  effect ;  a  large  stone  dropped  upon  the  ice 
crushes  it.  An  empty  car  in  motion  is  much  more  easily  stopped 
than  a  loaded  car.  We  dread  the  approach  of  large  masses 
because  we  instinctively  associate  with  them  a  large  amount  of 
motion  or  force.  It  is  evident  that  if  two  bodies  move  with  the 
same  speed,  there  is  a  greater  quantity  of  motion  in  that  which 
contains  the  greater  quantity  of  matter,  just  as  there  is  more 
heat  in  a  gallon  of  water  than  in  a  pint  of  water,  when  both  have, 
the  same  temperature. 

Again,  we  have  a  similar  dread  of  masses  moving  with  great 
velocities.  A  ball  tossed  is  a  different  affair  from  a  ball  thrown. 
Our  experience,  then,  teaches  us  that:  the  quantity  of  motion,  or, 
in  a  word,  the  momentum  a  body  may  have,  depends  upon  its 
mass  and  velocity'^  For  example,  a  large  mass,  moving  slowly, 
has  great  momentum,  but  the  same  mass-  will  have  twice  the 
momentum  if  its  velocity  is  doubled  ;  again,  a  small  mass,  mov- 
ing swiftly,  has  great  momentum,  but  its  momentum  is  increased 
in  proportion  as  its  mass  is  increased. 

If  the  motion  of  a  mass  weighing  lk,  having  a  velocity  of  lm 
per  second,  is  taken  as  a  unit  of  momentum,  then  a  mass  weigh- 
ing 5k,  moving  with  the  same  velocity,  would  have  a  momentum 
of  5  ;  and  if  the  latter  mass  should  have  a  velocity  of  10m  per 
second,  its  momentum  would  be  5  x  10  =  50.  Hence,)  the  nu- 
merical value  of  momentum  is  found  by  multiply  \v\(j  units  of  mass 


116  DYNAMICS. 

by  units  of  velocity^    There  is  no  name  for  the  unit  of  momen 
turn.     We  return  to  this  subject  on  page  123. 

QUESTIONS  AND   PROBLEMS. 

1.  Compare  the  momenta  of  a  car  weighing  50  tons,  moving  10  ft. 
per  minute,  and  a  lump  of  ice  weighing  5  cwt.,  at  the  end  of  the  third 
second  of  its  fall. 

2.  Why  are  pile-drivers  made  heavy?    Why  raised  to  great  hights? 

3.  A  boy  weighing  25k  must  move  with  what  velocity  to  have  the 
same  momentum  that  a  man  has  weighing  80k  running  at  the  rate  of 
10km  per  hour? 

4.  A  body  has  a  certain  momentum  after  falling  through  a  certain 
space.      How  many  times  this  space  must  it  fall  to  double  its  mo- 
mentum? 

§  86.  Third  law  of  motion.  — It  has  been  shown  (page  88) 
that  motion  cannot  originate  in  a  single  body,  but  arises  from 
mutual  action  between  two  bodies.  For  example,  a  man  can  lift 
himself  by  pulling  on  a  rope  attached  to  some  other  object,  but 
not  by  his  boot-straps,  or  a  rope  attached  to  his  feet.  When- 
ever one  body  receives  motion,  another  body  always  parts  with 
motion,  or  is  set  in  motion  in  an  opposite  direction  ;  that  is,  in 
every  change  in  regard  to  motion  there  are  always  at  least  two 
bodies  oppositely  affected^ 

Experiment.  Float  two  blocks  of  wood  of  unequal  masses  on 
water,  connecting  them  by  a  stretched  rubber  band.  Let  go  the  blocks, 
and  the  band  will  set  both  in  motion,  but  the  smaller  block  will  have 
the  greater  velocity. 

A  man  in  a  boat  weighing  one  ton  pulls  at  one  end  of  a  rope,  the 
other  end  of  which  is  held  by  another  man,  who  weighs  twice  as  much 
as  the  first  man,  in  a  boat  weighing  two  tons :  both  boats  will  move 
towards  each  other,  but  in  opposite  directions ;  the  lighter  boat  will 
move  twice  as  fast  as  the  heavier,  but  with  the  same  momentum. 

If  the  boats  are  near  each  other,  and  the  men  push  each  other's  boats 
with  oars,  the  boats  will  move  in  opposite  directions,  though  with  dif- 
ferent velocities,  yet  with  equal  momenta. 

The  opposite  impulses  received  by  the  bodies  concerned  are 
usually  distinguished  by  the  terms  action  and  reaction.  We 


THIBD   LAW   OF  MOTION.  117 

measure  these  by  their  momenta.  As  every  force  is  either  a 
push  or  a  pull  (§  12),  and  produces  equal  momenta  in  two 
bodies  in  opposite  directions,  hence,  the 

THIRD  LAW  OF  MOTION  :  \  To  every  action  there  is  an  equal 
and  opposite  reaction.  | 

The  application  of  this  law  is  not  always  obvious.  Thus,  the 
apple  falls  to  the  ground  in  consequence  of  the  mutual  attrac- 
tion between  the  apple  and  the  earth.  The  earth  does  not 
appear  to  fall  toward  the  apple.  But,  allowing  that  their  mo- 
menta are  equal,  we  are  not  surprised  that  the  motion  of  the 
earth  is  imperceptible,  when  we  reflect  that  the  velocity  of  the 
earth  must  be  as  many  times  less  than  that  of  the  apple  as 
the  mass  of  the  apple  is  less  than  that  of  the  earth.  (Compare 
§20.) 

QUESTIONS. 

1.  The  velocity  of  the  rebound  or  "  kick"  of  a  gun  is  slight  when 
compared  with  the  velocity  of  the  ball.     Why? 

2.  In  rowing  a  boat,  what  are  the  opposite  results  of  the  stress 
between  the  oar  and  the  water? 

3.  Point  out  the  results  of  the  action  and  reaction  that  occur  when 
a  person  leaps  from  the  ground. 

Fig.  94. 


4.  If  there  were  no  ground  or  other  object  beneath  him,  and  he 
were  motionless  in  space,  could  he  put  himself  in  motion?    Why? 

5.  A  boy,  running,  strikes  his  head  against  another  boy's  head. 
Which  is  hurt?    Why? 

6.  Suspend  two  balls  of  soft  putty  of  equal  weight,  A  and  B  (Fig. 
94).     Draw  A  one  side,  and  let  it  fall  so  as  to  strike  B.    Both  balls 


118  DYNAMICS. 

will  then  move  on  together ;  with  what  momentum  compared  with  A's 
momentum  when  it  strikes  Bfj 

7.  What  will  be  the  momentum  of  each  ball  after  A  strikes  B,  com- 
pared with  A's  momentum  when  it  strikes  B? 

8.  How  will   their  velocity  compare  with  A's  velocity   when   it 
strikes  B? 

9.  Raise  A  and  B  equal  distances  in  opposite  directions,  and  let  fall 
so  as  to  collide.    Both  balls  will  instantly  come  to  rest  after  collision. 
Show  that  this  result  is  consistent  with  the  third  law  of  motion. 

10.  Substitute,  for  the  inelastic  putty  balls,  ivory  billiard  balls,  which 
are  highly  elastic.     Let  A  strike  B.    Then  B  goes  on  with  A's  original 
velocity,  while  A  is  brought  to  rest.     Show  that  this  result  is  consis- 
tent with  the  third  law  of  motion. 

11.  Suspend  four  ivory  balls,  C,  D,  E,  and  F.     Let  C  strike  D.    D 
eventually  receives  all  of  C's  momentum,  and  instantly  communicates  it 
to  E,  E  to  F,  and  F,  having  nothing  to  which  to  communicate  it,  moves 
with  C's  original  velocity.    Trace  the  actions  and  reactions  throughout. 

12.  What  would  happen  if  the  four  balls  were  inelastic? 

§  87.  Law  of  reflection.  —  Experiment  1.  Hold  D  (Fig.  94) 
firmly  in  its  place,  and  allow  C  to  strike  it.  D  being  immovable,  C's 
entire  momentum  is  spent  in  compressing  the  balls,  and,  on  recovering 
their  shape,  C  is  thrown  back  to  its  starting-point  at  C'.  But  in  this 
case  the  hand  exerts  as  much  force  to  prevent  the  motion  of  D  as 
95  would  be  necessary  to  project  C  to  C'.  j  Whan 

an  elastic   body  strikes  another  fixed  elastic 
body,  it  rebounds  with  its  original  force. 

Experiment  2.  Lay  a  marble  slab  A  (Fig. 
95)  upon  a  table,  and  roll  an  ivory  ball  in  the 
line  D  C,  perpendicular  to  the  surface  of  the 
slab ;  the  ball  rebounds  in  the  same  line  to  D. 
Roll  the  ball  in  the  line  B  C ;  it  rebounds  in 
the  line  C  E.  The  angle  BCD,  which  its  for- 
ward path  makes  with  DC,  a  perpendicular  to  the  surface  struck,  is 
called  the  angle  of  incidence.  The  angle  ECD,  which  its  retreating 
path  makes  with  the  same  perpendicular,  is  called  the  angle  of  reflection. 

It  is  found  by  measurement  that  these  angles  are  equal  when 
the  two  bodies  are  perfectly  elastic.  This  equality  is  expressed 
by  the  LAW  OF  REFLECTION  :  \When  the  striking  body  and  the  body 
struck  are  perfectly  elastic,  the  angle  of  reflection  is  equal  to  the 
angle  of  incidence^ 


WORK.  119 


XV.    WORK  AND  ENERGY. 

§  88.  Work.  —  We  have  learned  (page  44)  that  a  force  may 
produce  either  motion  or  pressure  (or  tension),  or  it  may  produce 
both  effects  at  the  same  time  and  in  the  same  body.  But  a  force  does 
work,  in  the  sense  in  which  this  term  is  used  in  science,  only  when  it 
produces  motion.  A  person  may  support  a  weight  for  a  time  and 
become  weary  from  the  continuous  application  of  force  to  prevent  the 
weight  from  falling,  or,  in  other  words,  to  prevent  the  force  of  gravity 
from  doing  work,  but  he  accomplishes  no  work,  because  he  effects  no 
change,  i.e.,  causes  no  motion.  The  body  that  is  moved  is  said  to  have 
work  done  upon  it ;  and  the  body  that  moves  another  body  is  said  to  do 
work  upon  the  latter.  When  the  heavy  weight  of  a  pile-driver  is 
raised,  work  is  done  upon  it ;  when  it  descends  and  drives  the  pile 
into  the  earth,  work  is  done  upon  the  pile,  and  the  pile  in  turn  does 
work  upon  the  matter  in  its  path. 

Whenever  a  force  causes  motion,  it  does  work.  A  force  may  act  for  an 
indefinite  time  without  doing  any  work;  but  whenever  a  force  acts 
through  space,  work  is  done.  Force  and  space  (or  distance)  are  essen- 
tial elements  of  work,  and  are  naturally  the  quantities  employed  in 
estimating  work.  A  given  force  acting  through  a  space  of  one  meter 
will  do  a  certain  amount  of  work ;  it  is  evident  that  the  same  force 
acting  through  a  space  of  two  meters  will  do  twice  as  much  work. 
Hence  the  general  formula, 

W  =  FS,  (1) 

in  which  W  represents  the  work  done,  F  the  force  employed,  and  S 
the  space  through  which  the  force  acts. 

In  case  a  force  encounters  resistance,  the  magnitude  of  the  force 
necessary  to  produce  motion  depends  upon  the  amount  of  resistance. 
Indeed,  in  cases  in  which  the  body  having  been  moved  through  a 
given  space  comes  to  rest  in  consequence  of  resistance,  the  entire 
work  clone  upon  the  body  is  often  more  conveniently  determined  by 
multiplying  the  resistance  by  the  space  through  which  it  is  overcome,  and 
our  formula  becomes  by  substitution  of  resistance,  R,  for  the  force 

which  overcomes  it, 

W  =  RS.  (2) 

For  example,  a  ball  is  shot  vertically  upward  from  a  rifle  in  a  vacuum ; 
the  work  done  upon  the  ball  may  be  estimated  by  multiplying  the 
average  force  (difficult  to  ascertain)  exerted  upon  it  by  the  space 
through  which  the  force  acts  (a  little  greater  than  the  length  of  the 
barrel),  or  by  multiplying  the  resistance  offered  by  gravity,  i.e.,  its 
weight  (easily  ascertained)  by  the  distance  the  ball  ascends.  Also,  in 


120  DYNAMICS. 

case  the  motion  produced  is  uniform,  the  resistance  and  the  force  are 
equal,  and  it  is  immaterial  which  formula  is  used.  When  there  is  no 
resistance  and  the  only  effect  is  acceleration,  as  when  a  body  falls 
freely  in  a  vacuum,  we  must  estimate  the  work  done  (in  this  case  by 
gravity)  by  the  first  formula.  When  it  is  required  to  estimate  only 
that  part  of  the  work  done  in  producing  acceleration,  the  formulas 
given  on  page  124  will  be  found  convenient,  work  being  substituted 
for  energy,  inasmuch  as  both  are  measured  by  the  same  units. 

§  89.  Unit  of  work. — We  shall  first  consider  the  unit  em- 
ployed when  resistance  is  taken  as  one  of  the  elements  of  work.  (In 
§  96  will  be  defined  the  unit  usually  employed  when  the  force  is 
employed  as  a  factor  of  work.)  The  unit  of  work  adopted  by  the 
French  is  the  work  done  in  raising  lk  through  a  vertical  hight  of  lm. 
It  is  called  a  kilogrammeter  (abbreviated  ksm).  The  English  unit  of 
work  is  that  done  in  raising  one  pound  one  foot,  and  is  called  a  foot- 
pound. The  kilogrammeter  is  about  1\  (more  accurately,  7.233)  times 
greater  than  the  foot-pound.  Now,  since  the  work  done  in  raising  lk 
lm  high  is  lksm,  the  work  of  raising  it  10m  high  is  10ksm,  which  is  the 
same  as  the  work  done  in  raising  10k  lm  high;  and  the  same,  again,  as 
raising  2k  5m  high. 

There  are  many  other  kinds  of  work  besides  that  of  raising  weights. 
But  since,  with  the  same  resistance,  the  work  of  producing  motion  in 
any  other  direction  is  just  the  same  as  in  a  vertical  direction,  it  is 
easy,  in  all  cases  in  which  the  two  elements  of  work  (viz.,  resistance 
and  space)  are  known,  to  find  the  equivalent  in  work  done  in  raising  a 
weight  vertically.  By  thus  securing  a  common  standard  for  measure- 
ment of  work,  we  are  able  to  compare  auy  species  of  work  with  any 
other.  For  instance,  let  us  compare  the  work  done  by  a  man  in  sawing 
through  a  stick  of  wood,  whose  saw  must  move  101 '  against  an  average 
resistance  of  12k,  with  that  done  by  a  bullet  in  penetrating  a  plank  to  a 
depth  of  2cm  against  an  average  resistance  of  200k.  Moving  a  saw 
10m  against  12k  resistance  is  equivalent  to  raising  12k  10ra  high,  or 
doing  120k£m  of  work ;  a  bullet  moving  2cm  against  200k  resistance  does 
as  much  work  as  is  required  to  raise  200k  2cm  high,  or  200  X  .02  =  4kg™ 
of  work.  120  -f-  4  =  30  times  as  much  work  done  by  the  sawyer  as  by 
the  bullet. 

§  90.  Rate  of  doing  work. — In  estimating  the  total 
amount  of  work  done,  the  time  consumed  is  not  taken  into  con- 
sideration. The  work  done  by  a  hod-carrier,  in  canying  1,000 
bricks  to  the  top  of  a  building,  is  the  same  whether  he  does  it  in 


POTENTIAL  AND   KINETIC   ENERGY.  121 

a  day  or  a  week.  But  in  estimating  the  power  of  any  agent  to 
do  work,  as  of  a  man,  a  horse,  or  a  steam-engine,  in  other  words, 
the  rate  at  which  it  is  capable  of  doing  work,  it  is  evident  that 
time  is  an  important  element.  The  work  done  by  a  horse,  in 
raising  a  barrel  of  flour  20  feet  high,  is  about  4000  ft.-lbs.  ; 
but  even  a  mouse  could  do  the  same  amount  of  work  in  time. 
The  unit  in  which  rate  of  doing  work  is  usually  expressed  is  a 
horse-power.  Early  tests  showed  that  a  very  strong  horse  may 
perform  33,000  ft.-lbs.  of  work  in  one  minute.  So  1  horse- 
power ==  33,000  ft.-lbs.  per  minute  =  550  ft.-lbs.  per  second  = 
about  4570kgm  per  minute  =  about  76kgm  per  second. 

§  91.  Energy.  —  The  energy  of  a  body  is  its  capacity  of 
doing  work,  and  is  measured  by  the  work  it  can  do.  Doing 
work  usually  consists  in  a  transfer  of  motion,  or  energy,  from 
the  body  doing  work  to  the  body  on  which  work  is  done.  Wher- 
ever we  find  matter  in  motion,  whether  in  the  solid,  liquid,  or 
gaseous  state,  we  have  a  certain  amount  of  energy  which  may 
often  be  made  to  do  useful  work. 

§  92.  Potential  and  kinetic  energy.  —  Place  a  stone, 
weighing  (say)  10k,  on  the  floor  before  you ;  it  is  devoid  of 
energy,  powerless  to  do  work.  Now  raise  it,  and  place  it  on  a 
shelf  (say)  2m  high  ;  in  so  doing  you  perform  20kgm  of  work  on 
it.  As  you  look  at  it,  lying  motionless  on  the  shelf,  it  appears 
as  devoid  of  energy  as  when  lying  on  the  floor.  Attach  one  end 
of  a  cord  3m  long  to  it,  and,  passing  it  over  a  pulley,  wind  2m 
of  the  string  around  the  shaft  connected  with  a  sewing-machine, 
coffee-mill,  lathe,  or  other  convenient  machine.  Suddenly  with- 
draw the  shelf  from  beneath  the  stone.  It  moves,  it  sets  in 
motion  the  machine,  and  you  may  sew,  grind  coffee,  turn  wood, 
etc.,  with  the  power  given  to  the  machine  by  the  stone. 

Surely,  the  work  done  on  the  stone  in  raising  it  was  not  lost ; 
the  stone  pays  it  back  while  descending.  There  is  a  very  im- 
portant difference  between  the  stone  lying  on  the  floor,  and  the 


122  DYNAMICS. 

stone  lying  on  the  shelf :  the  former  is  powerless  to  do  work ; 
the  latter  can  do  work.  Both  are  alike  motionless,  and  you  can 
see  no  difference,,  except  an  advantage  that  the  latter  has  over 
the  former  in  position.  What  gave  it  this  advantage?  Work. 
A  body,  then,  may  possess  energy  due  merely  to  ADVANTAGE  OF 
POSITION,  derived  always  from  work  bestowed  upon  it.  So  a  body 
at  rest  is  not  necessarily  devoid  of  energy.  In  the  stone  lying 
passively  on  the  shelf  there  exists  a  power  to  do  work  as  real  as 
that  possessed  by  the  stone  which,  falling  freely,  has  acquired 
great  velocity. 

We  see,  then,  that  energjT  ma}'  exist  in  either  of  two  widely 
different  states,  and  yet  be  as  real  in  one  case  as  in  the  other. 
It  may  exist  as  actual  motion,  either  visible,  as  in  mechanical 
motion,  or  invisible,  as  in  the  molecular  motions  called  heat ;  or 
it  ma}r  exist  in  a  stored-u2)  condition,  as  in  the  stone  lying  on  the 
shelf.  In  the  former  case  it  is  called  kinetic  (moving)  or  actual 
energy ;  in  the  latter,  it  is  called  potential  energy,  or  energy  of 
position. 

We  are  as  much  accustomed  to  store  up  energy  for  tuture  use 
as  provisions  for  the  winter's  consumption.  We  store  it  when 
we  wind  up  the  spring  or  weight  of  a  clock,  to  be  doled  out 
gradually  in  the  movements  of  the  machinery.  We  store  it 
when  we  bend  the  bow,  raise  the  hammer,  condense  air,  and 
raise  any  body  above  the  earth's  surface. 

How,  then,  is  energy  stored  in  a  body  ?  Only  at  the  expense 
of  work  done  upon  it.  The  force  of  gravitation  is  employed  to 
do  work,  as  when  mills  are  driven  by  the  power  of  falling 
water ;  but  the  water  is  first  deposited  on  the  hillside  by  the 
energy  of  the  sun's  heat.  Elasticity  of  springs  is  emplo}'ed  as 
a  motive  power  ;  but  elasticity  is  due  to  an  advantage  of  position 
which  the  molecules  of  springs  have  acquired  in  consequence  of 
force  applied  to  them. 

We  conclude,  then,  that  a  body  %>ossesses  potential  energy 
•when,  in  virtue  of  work  done  upon  it,  it  occupies  a  position  of 
advantage,  or  its  molecules  occupy  positions  of  advantage,  so  tliat 


FORMULA   FOR   ENERGY.  123 

the  energy  expended  can  be  at  any  time  recovered  by  the  return 
oj  the  body  to  its  original  position,  or  by  the  return  of  its  mole- 
cules to  their  original  positions. 

<•* 

§93.  Energy  contrasted  with  momentum. —Problem. 
A  bullet  weighing  30s  is  shot  with  a  velocity  of  98m  per  second  from  a 
gun  weighing  4k ;  required  the  momentum  and  the  energy  of  both  the 
bullet  and  the  gun,  and  the  velocity  of  the  gun.  Solution :  Using  the 
kilogram,  the  meter,  and  the  second  as-  units,  the  momentum  of  the 
ball  is  .03  x  98  =  2.94  units.  If  the  ball  were  shot  vertically  upward, 

QO 

its  velocity  would  diminish  9.8m  per  second;  so  it  would  rise  — =10 

9.8 

seconds,  and,  therefore,  before  its  energy  is  expended,  to  a  hight 
of  (§  78)  4.9m  x  102  =  490m.  Hence,  its  energy  at  the  outset  is 
.03x490=  14.7ksm.  Similarly  for  the  gun,  by  the  third  law  of  mo- 
tion its  momentum  must  be  just  the  same  as  that  of  the  ball,  2.94 
units;  its  velocity  is  therefore  2.94  -f-  4  =  .735™  per  second.  Then 

T  = '— -  =  .075  second ;  the  hight  (supposing  the  gun  to  be  raised  verti- 

9.8 

cally  by  the  impulse  received)  =  4.9  x  -0752  =  .02766m ;  and  its  energy 
=  4  X  .02766=  .1102kgm. 

While,  therefore,  the  momenta  generated  in  the  two  bodies  by  the 

burning  of  the  powder  are  equal,  the  energy  of  the  bullet  is  =  133£ 

.  1 102 

times  that  of  the  gun.  (Why  are  the  effects  produced  by  the  bullet 
more  disastrous  than  those  produced  by  the  recoil  of  the  gun?) 

§  94.  Formula  for  energy.  —  We  can  find,  as  in  the  above 
example,  to  what  vertical  hight  a  body  having  a  given  velocity 
would  rise,  and  thus  in  all  cases  determine  its  energy ;  but  a 
formula  may  be  obtained  which  will  give  the  same  result  with 
less  trouble:  thus,  substituting  g  for  k  in  Formula  1  (§  78), 
V  =  #T;  hence,  v  V2 

T=-,  orT2=  — . 
9  92 

Again,  S  =  ^#T2 ;  substituting  the  value  of  T2  in  this  equation, 
we  have  V2  V2 


124  DYNAMICS. 


But  energy  =  WS    (weight  into  .bight)  ;  substituting  for  S  in 
this  equation  its  value,  we  have, 

(1)  Energy  = 


Farther  on,  we  shall  see  that  W  =  M^;  substituting  f  or  W  in 
the  last  equation  its  value,  we  have,  also, 

(2)  Energy  =  *Z1. 

It  is  evident  that,  when  the  weight  (  W)  or  mass  (M)  of  a  body 
remains  the  same,  its  energy  is  proportional  to  the  square  of  its 
velocity,  while  its  momentum,  as  we  have  learned,  is  proportional 
to  its  velocity.  In  other  words,  the  effect  of  increasing  the  velocity 
of  a  moving  body  would  seem  to  be  to  increase  its  working  power 
much  more  rapidly  than  its  momentum.  Is  this  practically  true  ? 

Experiment.  Fill  an  ordinary  water-pail  with  moist  clay.  Let  a 
leaden  bullet  drop  upon  the  clay  from  a  hight  of  .5m.  Then  drop  the 
same  bullet  from  a  hight  of  2m,  or  four  times  the  former  hight,  in  order 
that  it  may  acquire  twice  the  velocity.  In  the  latter  case  it  penetrates 
to  four  times  the  depth  that  it  did  in  the  former. 

So  it  appears  that  the  energy  of  a  moving  body  varies,  not  as 
its  velocity,  but  as  the  square  of  its  velocity.  Doubling  the 
velocity  multiplies  the  energy  fourfold  ;  trebling  the  velocity 
multiplies  it  ninefold,  and  so  on  ;  but  the  corresponding  mo- 
mentum is  multiplied  only  twofold,  threefold,  etc.  A  bullet 
moving  with  a  velocity  of  400  feet  per  second,  will  penetrate, 
not  twice,  but  four  times,  as  far  into  a  plank  as  one  having  a 
velocity  of  200  feet  per  second.  A  railway  train,  having  a 
velocity  of  20  miles  an  hour,  will,  if  the  steam  is  shut  off,  con- 
tinue to  run  four  times  as  far  as  it  would  if  its  velocity  were  10 
miles  an  hour.  The  reason  is  now  apparent  why  light  sub- 
stances, even  so  light  as  air,  exhibit  great  energy  when  their 
velocity  is  great. 

§  95.  Measure  of  a  force.  —  Commonly  we  measure  forces 
by  a  spring  balance,  and  say  that  the  force,  for  instance,  with 


MEASURE   OF  A  FORCE.  125 

which  a  horse  draws  a  wagon  is  50k  ;  that  is,  a  spring  interposed 
between  the  horse  and  the  wagon  is  stretched  just  as  much  as  it 
would  be  by  the  force  of  gravity  acting  on  a  mass  of  50k  hung 
from  the  spring.  But  often  it  is  impossible  to  measure  the 
force  except  by  the  motion  it  produces.  Experience  has  shown 
that  a  useful  and  accurate  measure  of  a  force  is  the  momentum  it 
produces  or  destroys  in  a  second;  if  the  body  is  already  in  mo- 
tion, we  must  say  the  change  of  momentum  produced  in  a  second. 

For  example,  gravity  we  know  will  impart  in  three  seconds, 
to  a  body  having  a  mass  of  (say)  5g,  and  free  to  fall,  a  velocity 
of  3  x  980cm  per  second ;  that  is,  the  momentum  generated  is 
5  x  3  x  980.  Then,  by  definition  above,  the  measure  of  the 
force  of  gravity  on  the  body  is  SJLZ^BSO.  =  5  x  980.  When  the 
centimeter,  gram,  and  second  are  taken  as  the  units  of  length, 
mass,  and  time  respectively,  the  s}Tstem  of  units  of  measurement 
based  on  them  is  called  the  C.G.S.  system,  and  in  it  the  unit 
of  force  is  called  a  dyne. 

A  dyne  is  that  force  which,  acting  for  a  second,  will  give  to  a 
gram  of  matter  a  velocity  of  one  centimeter  per  second.  In  the 
example  above  we  have  a  force  of  5  x  980  =  4900  dynes. 

We  can  almost  as  easily  graduate  a  spring  balance  to  indi- 
cate forces  in  dynes  as  in  pounds ;  and  then  we  have  a  unit 
which  is  constant  wherever  we  go  on  the  earth  or  above  it. 
(Compare  §  21.) 

The  gravity  unit  of  force  is  the  weight  of  any  unit  of  mass, 
e.g.,  a  gram,  kilogram,  pound,  or  ton.  In  distinction  from 
gravity  units,  the  C.G.S.  units  are  called  absolute  units.  Gravity 
units  are  easily  changed  to  absolute  units  ;  thus  in  the  Northern 
States  the  force  of  gravity  acting  upon  lg  of  matter  free  to  fall 
will  give  it  an  acceleration  of  velocity  of  980cm  per  second ;  hence 
in  these  latitudes  the  gravity  unit  is  equal  to  980  absolute  units. 

Returning  to  our  example,  represent  5g,  the  mass  of  the  body 
moved  by  M  ;  by  g,  980cm  per  second,  the  acceleration  produced 
by  gravity ;  and  by  W,  the  weight,  or  F,  the  force  :  then 
W  =  F  =  M. 


126  DYNAMICS. 

The  equation  is  a  general  one  ;  that  is,  whenever  any  two  of  the 
three  quantities  specified  are  known,  the  third  may  be  computed 

If  the  force  acts,  not  against  gravity,  but  against  resistances 
considered  as  constant,  such  as  the  forces  shown  in  cohesion, 
elasticity,  etc.,  the  equation  will  still  be  true,  only  g  should  be 
replaced  by  some  other  letter,  as  a. 

Now  let  us  learn  what  is  the 

§  96.  Measure  of  the  effect  of  a  force.  —  One  measure  we 
know  alread}',  —  the  product  of  the  force  into  the  distance 
through  which  it  acts  ;  that  is,  the  work  done,  or  the  energy 
imparted  to  the  body  moved,  is  a  measure  of  the  effect  of  a  force. 
If  the  force  is  measured  in  dynes,  and  the  distance  is  centi- 
meters, the  work  done  will  be  expressed  in  a  C.G.S.  unit  called 
an  erg.  An  erg  is  the  work  done  or  energy  imparted  by  a  force 
of  one  dyne  working  through  a  distance  of  one  centimeter.  Be- 
sides the  erg  we  have  the  common  gravitation  units,  the  kilo- 
grammeter,  and  foot-pound  ;  that  is,  we  have  another  measure  just 
as  we  ma  have  various  kinds  of  measures  for  common  things  ; 
just  as,  for  instance,  we  may  express  lengths  in  inches,  meters, 
or  miles  ;  masses,  in  grains  or  pounds,  etc. 

Experiment  1.  Suspend  by  a  long  cord  a  heavy  body,  —  10k  or  more, 
—  and  with  a  string  attached  to  the  body  draw  it  to  one  side,  pulling 
for  two,  four,  and  six  seconds,  and  let  go.  The  longer  you  pull  the 
greater  is  the  velocity  given  to  the  body,  provided  it  is  not  moved  far 
from  its  place  of  rest. 

Experiment  2.  Suspend  by  a  string  lm  long  a  stone  whose  mass  is 
(say)  5k.  Attach  to  the  stone  a  No.  36  cotton  thread ;  this  will  sup- 
port about  lk.  Pull  the  ball  slowly  to  one  side ;  when  it  has  been 
drawn  about  20cm  from  its  place  of  rest,  the  thread  will  break  and  the 
ball  will  swing  back  to  the  other  side  like  a  pendulum,  and  so  when  it 
passes  through  its  lowest  point  it  has  a  definite  momentum. 

Attach  new  pieces  of  thread,  and  pull  more  and  more  quickly,  break- 
ing the  thread  each  time ;  the  motion  produced  is  less  and  less.  As 
the  string  is  straightened  the  pull  on  it  increases  from  zero  to  lk;  so 
the  average  force  each  time  is  about  the  same;  in  gravitation  uuits, 
nearly  or  exactly  |k.  Here,  as  before,  with  the  same  force,  the  momen- 
tum produced  varies  as  the  time  during  which  the  force  acts. 


MEASURE   OF  THE  EFFECT   OF   A  FORCE.  127 

But  if  we  use  stronger  and  stronger  threads,  we  may  pull  more  and 
more  quickly  than  at  first,  and  yet  give  to  the  ball  just  the  same  mo- 
mentum as  at  first;  that  is,  the  effect  of  a  greater  force  acting  for  a 
shorter  time  is  to  produce  the  same  momentum. 

So  far  then  as  our  experiments  go,  they  teach  that  the  product 
of  a  force  into  the  time  it  acts,  or  the  momentum  produced,  is  a 
measure  of  the  effect  of  a  force.  We  may  draw  the  same  conclu- 
sion from  our  last  equation,  F  =  M#  :  multiply  both  sides  by  T, 
the  time  during  which  the  force  acts,  and  we  have  FT  =  M#T 
=  MV  =  Momentum  (§  85).  If  T  equals  one  second,  we  see 
that  the  momentum  of  a  moving  body  is  the  measure  of  the  force 
that  would  in  one  second  give  it  this  motion.  It  is  evident 
that  if  motion  is  to  be  produced  by  a  force  acting  for  a  very 
short  time,  the  force  must  be  enormous. 

We  have,  then,  two  measures  of  the  effect  of  a  force,  —  mo- 
mentum and  energy.  The  first  is  found  by  multiplying  the  force 
by  the  time  it  acts  ;  the  second,  by  multiplying  the  force  by  the 
space  through  which  it  acts.  The  latter  can  also  be  found  by 
multiplying  the  momentum  by  one-half  the  velocity.  One  is 
MV  ;  the  other  is  -J-MV2.  Which  is  the  correct  measure?  Both 
are  correct ;  so  the  question  now  is,  Which  is  the  more  useful  ? 
P^xperience  shows  that  momentum  is  a  useful  measure  only  in 
cases  where  the  force  acts  all  the  time  in  the  line  of  motion,  as 
in  falling  bodies,  or  where  it  acts  for  so  short  a  time  that  the 
body  does  not  sensibly  change  its  position  during  the  action,  as 
in  the  cases  of  a  blow,  a  jerk,  collision'  between  balls,  etc. 
Experience  further  shows  that  energy  in  all  cases  gives  a  useful 
measure. 

§  97.  Summary  of  mechanical  units,  and  formulas  for 
their  determination.1  —  The  following  tables  show  the  quanti- 
ties measured,  the  unit  of  each  in  the  C.G.S.  system,  and  the 
formulas  for  the  determination  of  the  derived  quantities  :  — 

i  It  is  not  expected  that  pupils  of  the  ordinary  high  school  will  master  this  sec- 
tion; yet  they  may  frequently  find  it  convenient  for  reference,  while  the  more 
advanced  student  cannot  fail  to  be  greatly  profited  by  its  careful  study. 


128  DYNAMICS. 

FUNDAMENTAL  QUANTITIES  AND  UNITS. 

Length  (L  or  S) lcm. 

Mass  (M) l«. 

Time  (T) 1  sec. 

DERIVED  QUANTITIES,  UNITS,  AND  FORMULAS. 

Velocity  (V)  =  rate  of  motion ;  unit,  lcm  per  sec. ;  in  uniform  motion, 
V  =  |-  (1) 

Acceleration  (A)  =  rate  of  change  in  velocity ;  unit,  an  increase  of 
velocity  in  1  sec.  of  lcm  per  sec. ;  body  starting  from  rest  under 

constant  force,  A  =  —  •  (2) 

Force  (F) ;  unit,  1  dyne  =  a  force  that  in  1  sec.  imparts  to  1«  a  velocity 
of  lcm  per  sec. ;  .  •.  F  =  M  A.  (3) 

Work  or  Energy  (E) ;  unit,  1  erg  =  the  work  done  by  1  dyne  working 
through  lcm;  .-.  E  =  MAS  =  FS.  (4) 

Rate  of  doing  work,  or  Work  Power  (P) ;  unit,  1  erg  per  sec.; 
MAS 

r  —        rp      '  (°) 

Momentum;  unit,  is  moving  with  a  velocity  of  lcm  per  sec.,  or  that 
produced  by  1  dyne  in  1  sec. ;  Momentum  =  MV. 

M  V 
From  (2)  and  (3)  we  have  the  very  useful  equations,  F  =  -=-  and 

FT 

V=— •  (6)  and  (7) 

A  body,  mass  M,  acted  upon  by  the  force  F,  starting  from  rest  will 

FT 
acquire  in  time  T  a  velocity  V  =  -r—  •    The  acceleration,  which 

•p  M 

from  (3)  is  =  — ,  is  a  constant  quantity,  and  the  whole  space 

passed  over  will  be  equal  to  the  time  T  multiplied  by  the  mean 
velocity.    The  latter  is  one-half  the  final  velocity;  hence,  mean 

FT  FT2 

V  =  — ,  and  S  =  -r-ri  (an  equation  of  great  importance).  (8) 

&  JVl  1  JM 

To  find  an  expression  for  the  energy  of  a  moving  body  combine  (4)  and 

F2  T2  M  V2 

(8):  W  =  y^-;  butFT  =  MV,  .-.  E  =  ±^—  (9) 

Anywhere  in  the  Northern  States,  the  weight  of  18  =  980  dynes. 
Ikgm  _  98,000,000  ergs ;  1  foot-pound  =  13,550,000  ergs. 
1  horse-power  =  447,000,000,000  ergs  per  min. 
i— 
§  98.   Transformation  of  energy.  —  In  the  operation  of 

raising  the  stone  (§  92) ,  kinetic  energy  is  transformed  into  poten- 


PHYSICS    DEFINED.  129 

tial  energy.  During  its  descent  it  is  re-transformed  into  kinetic 
energy.  If,  instead  of  being  attached  to  machinery,  and  thereby 
made  to  do  work,  the  stone  is  allowed  to  fall  freely,  it  acquires 
great  velocity.  On  striking  the  ground,  its  motion  as  a  body 
suddenly  ceases,  but  its  molecules  have  their  quivering  motions 
accelerated.  Mechanical  motion  is,  thereby,  transformed  into 
heat.  We  shall  often  have  occasion  to  examine  the  transforma- 
tions of  energy,  as  into  electric  energy,  heat,  etc.,  but  never  of 
momentum.  We  shall  study  Joule's  equivalent  (page  174), 
expressing  the  relation  between  the  unit  of  energy,  or  work, 
and  the  unit  of  heat ;  but  it  is  certain  that  there  is  no  relation 
between  the  latter  and  the  unit  of  momentum. 

§  99.  Physics  defined.  —  All  physical  phenomena  consist 
either  alone  in  transferences  of  energy  from  one  portion  of 
matter  to  another,  or  in  both  transferences  and  transformations 
of  energy.  Transformations  may  be  from  one  condition  of 
energy  to  another,  as  from  kinetic  to  potential ;  or  from  one 
phase  of  kinetic  energy  to  another,  as  from  mechanical  motion 
to  heat ;  or  both  may  occur,  as  when  the  falling  stone  does 
work,  a  part  of  its  energy  being  expended  in  producing  mechan- 
ical motion,  and  a  part  being  transformed  into  heat,  occasioned 
by  friction  of  the  moving  parts. 

Physics  is  that  branch  of  natural  science  which  treats  of  trans- 
ferences and  transformations  of  energy.  It  does  not,  however, 
in  its  usual  limitation,  include  a  group  of  phenomena  which  occur 
outside  the  earth,  and  also  a  group  whose  essential  character- 
istic is  an  alteration  in  the  nature  of  the  material  considered. 
The  study  of  the  former  group  is  the  object  of  Astronomy ;  of 
the  latter,  that  of  Chemistry. 

QUESTIONS  AND   PROBLEMS. 

1.  Does  the  energy  expended  in  raising  the  stones  to  their  places  in 
the  Egyptian  pyramids  still  survive? 

2.  What  kind  of  energy  is  that  contained  in  gunpowder? 

3.  What  transformation  of  energy  takes  place  in  burning  coal? 

4.  When  steam  works  by  expansion,  its  temperature  is  reduced.  Why? 


130  DYNAMICS. 

5.  How  much  work  is  clone  per  hour  if  80k  are  raised  4m  per  minute? 

6.  (a)  What  energy  must  be  imparted  to  a  body  weighing  50s  that  it 
may  rise  4  seconds?     (&)  How  many  times  as  much  energy  must  be 
imparted  to  the  same  body  that  it  may  ascend  5  seconds?     (c)  Why? 

7.  Compare  the  momenta,  in  the  two  cases  given  in  the  last  question, 
at  the  instants  the  body  is  thrown. 

8.  How  much  energy  is  stored  in  a  body  which  weighs  50k,  at  a 
hight  of  80m  above  the  earth's  surface? 

9.  How  much  energy  would  the  same  body  have  if  it  had  a  velocity 
"of  100m  per  second? 

10.  Suppose  it  to  fall  in  a  vacuum,  how  much  kinetic  energy  would 
it  have  at  the  end  of  the  fourth  second? 

11.  If  it  should  fall  through  the  air,  what  would  become  of  a  part  of 
the  energy? 

12.  A  projectile  weighing  25k  is  thrown  vertically  upward  with  an 
initial  velocity  of  29. 4m  per  second.     How  much  energy  has  it? 

13.  What  becomes  of  its  energy  during  its  ascent? 

14.  (a)  Compare  the  momentum  of  a  body  weighing  50k,  and  having 
a  velocity  of  2m  per  second,  with  the  momentum  of  a  body  weighing 
508,  having  a  velocity  of  100m  per  second.     (&)  Compare  their  ener- 
gies. 

15.  Which,  momentum  or  energy,  will  enable  one  to  determine  the 
amount  of  resistance  that  a  moving  body  may  overcome? 

16.  Explain  how  a  child  who  cannot  lift  30k  can  draw  a  carriage 
weighing  150k. 

17.  A  car  weighing  6000k  is  drawn  by  a  horse  with  a  speed  of  100™  per 
minute.     The  index  of  the  dynamometer  to  which  the  horse  is  attached 
stands  at  40k.     (a)  At  what  rate  is  the  horse  working?     (&)  Express 
the  rate  in  horse-powers.     (See  §  90.) 

18.  A  dynamometer  shows  that  a  span  of  horses  pull  a  plow  with 
a  constant  force  of  70k.     What  power  is  required  to  work  the  plow  if 
they  travel  at  the  rate  of  3km  per  hour? 

19.  What  horse-power  in  an  engine  will  raise  l,350,000k  5m  in  an 
hour? 

20.  How  long  will  it  take  a  3  horse-power  engine  to  raise  10  tons  50 
feet? 

21.  How  far  will  a  2  horse-power  engine  raise  1000k  in  10  seconds? 

22.  How  much  work  can  a  5  horse-power  engine  do  in  an  hour? 

23.  How  long  would  it  take  a  man  to  do  the  same  work,  the  amount 
of  work  a  man  can  do  in  a  day  being  about  90,000k^n? 

24.  If  you  would  increase  the  energy  of  a  moving  body  fourfold, 
how  much  must  you  increase  its  velocity? 


T.SO  -?:>.. 

USES   OF   MACHINES.  131 


XVI.     MACHINES. 

§  100.  Uses  of  machines.  —  Experiment  1.  Obtain  from  a 
hardware  store  two  or  three  pulleys,  and  arrange  apparatus  as  in  Figure 
96.  The  dynamometers  a  and  b  read  4  Ibs.  each,  showing  that  the 
power  (P)  employed  to  support  each  weight  (W)  of  8  Ibs.  is  just 
one-half  of  the  weight.1  .  If  the  power  applied  in  each  instance  is 
slightly  increased,  the  weights  will  rise.  Raise  each  of  the  weights 
and  measure  the  distances  traversed  respectively  by  W  and  P  in  each 
instance.  It  will  be  found  that  the  distance  that  W  moves  is  just  one- 
half  the  distance  that  P  moves;  i.e.,  if  W  rises  2  ft.,  P  must  move  4 
ft.  Now,  8  (Ibs.)  X  2  (ft.)  =  16  foot-pounds  of  work  done  on  W. 
Again,  4  (Ibs.)  x  4  (ft.)  =  16  foot-pounds  of  work  performed  by  P. 
It  thus  seems  that  the  work  applied  by  the  power  is  just  equal  to  the 

work  done  upon  the  weight. 
What  advantage  is  derived 
from  the  use  of  the  apparatus? 
It  has  been  proved  that  no  ad- 
vantage is  gained,  so  far  as  the 
amount  of  work  is  concerned. 
But  suppose  that  W  is  400 Ibs., 
and  that  the  utmost  power  (P) 
that  one  man  can  exert  is  200 
Ibs.  Then,  without  this  ap- 
paratus, the  services  of  two 
men  would  be  required ;  where- 
as one  man  could  raise  the 
weight  with  the  apparatus. 
The  advantage  gained  in  this 
case  would  seem  to  be  one  of 
convenience. 

Experiment  2.  Let  P  and 
W  of  A  exchange  places.  The 
index  of  the  dynamometer  a 
now  reaches  16  Ibs.  There 
seems  to  be  in  this  case  a  loss 
of  power,  for  a  power  of  16 
Ibs.  is  only  able  to  sustain  a  weight  of  8  Ibs.  But  so  far  no  work 
has  been  done.  (Why?)  Raise  W,  and  measure  the  distance  trav- 
ersed respectively  by  P  and  W.  P  moves  only  2  ft.  for  every  4  ft. 
that  W  moves.  Now,  2  (ft.)  x  16  (Ibs.)  =  32  foot-pounds  of  work 
1 A  small  allowance  must  be  made  for  the  weight  of  the  movable  pulleys. 


132 


DYNAMICS. 


done  by  P.  And  4  (ft.)  x  8  (Ibs.)  =  32  foot-pounds  of  work  done 
upon  W.  We  thus  learn  that,  when  the  power  is  employed  in  doing 
work,  there  is  really  no  loss  of  power  in  this  method  of  applying  the 
apparatus.  Is  there  any  advantage  gaiued  in  this  case  by  the  use  of 
apparatus?  We  found  that  W  moved  twice  as  far,  and  consequently 
with  twice  the  velocity,  that  P  moved. 

It  thus  appears  that,  if  it  should  be  desirable  to  move  a  weight  with 
greater  velocity  than  it  is  possible  or  convenient  for  the  power  to 
move,  it  may  be  accomplished  through  the  mediation  of  a  machine,  by 
applying  to  it  a  power  proportionately  greater  than  the  weight.  This 
apparatus  is  one  of  many  contrivances  called  machines,  through  the  medi- 
ation of  which  power  can  be  applied  to  resistance  more  advantageously 
than  when  it  is  applied  directly  to  the  resistance.  Some  of  the  many 
advantages  derived  from  the  use  of  machines  are :  — 

(1)  They  may  enable  us  to  overcome  a  large  resistance  with  a  compara 
tively  small  power  by  causing  the  power  to  move  through  a  proportionately 
greater  distance,  (i.e.  with  greater  velocity}  ;  or,  conversely,  they  may  enable 
us  to  secure  great  velocity  (i.e.  to  do  work  with  great  speed)  by  employing 
a  power  proportionately  greater  than  the  resistance. 

(2)  They  may  enable  us  to  employ  a  force  in  a  direction  that  is  more 
convenient  than  the  direction  in  which  the  resistance  is  to  be  moved. 

Fig.  97.  (3)   They  may  enable  us  to  employ  other'forces 

than  our  own  in  doing  work;  e.g.,  the  strength 
of  animals,  the  forces  of  wind,  water,  steam, 
etc.  (How  are  the  last  two  uses  illustrated  in 
Figure  97  ?) 

§  101.    Law  of  machines.  —  Let  P 
be   the   power   applied  to  a  machine,  p 
the  distance  through  which  it  moves  in 
a   given  time,  W  the  weight  moved  or 
external  resistance  overcome,  and  w  the 
distance   through   which   it   is  moved  in 
the  same  time  ;  then  the  mechanical  work 
applied  to  the  machine  is  Pp  (e.g., 
in  kilogrammeters  or  foot-pounds), 
and  the  mechanical  work  done  by 
the  machine  is  Ww.    Now  we  have 
learned  from  the  above  experiments  that  (1)  Pp  =Ww. 


LAW    OF   MACHINES.  133 

Hence  we  have  for  all  machines,  without  exception,  the.  follow- 
ing general  law  :  The  work  applied  to  a  machine  is  equal  to  the 
work  done  by  the  machine. 

No  machine,  therefore,  creates  or  increases  energy.  No  ma- 
chine gives  back  more  energy  than  is  spent  upon  it.  P  can  be 
made  as  small  as  we  please  by  taking  p  great  enough :  in  this 
case  we  see  that  in  proportion  as  power  is  gained,  time,  distance, 
or  velocity  is  lost.  On  the  other  hand,  W  remaining  the  same, 
w  (the  distance  traversed  by  W  in  a  given  time,  i.e.,  its  velocity) 
may  be  increased  indefinitely  by  taking  P  large  enough  :  in  this 
case,  as  velocity,  time,  or  space  is  gained,  power  is  lost.  -  A  ma- 
chine, then,  is  much  like  a  bank :  it  pays  out  no  more  thari  it 
receives.  A  bank  will  give  you  in  exchange  for  a  fifty-dollar 
note  fifty  one-dollar  notes ;  or,  for  fifty  one-dollar  notes,  de- 
posited successively,  it  will  return  to}T>u  a  fifty-dollar  note.  In 
a  similar  manner,  if  you  apply  to  a  machine  a  power  sufficient 
to  move  50  Ibs.  1  ft.,  you  may  get  from  it  the  ability  to  move 
1  Ib.  50  ft.  ;  or,  if  you  apply  to  a  machine  a  force  of  1  Ib.  suc- 
cessively through  50  ft.  of  space,  you  may  get  from  it  the  ability 
to  move  50  Ibs.  through  1  ft.  of  space. 

In  our  discussion  hitherto  we  have  ignored  the  internal  resist- 
ances, chiefly  due  to  friction,  which  exist  in  every  machine.  The 
whole  work  done  by  a  machine  is  practically  divided  into  two 
parts,  —  the  useful  part  and  the  wasted  part ;  the  former,  ex- 
pressed as  a  fraction  of  the  whole,  is  usually,  called  the  efficiency 
or  modulus  of  the  machine.  But  energy  is  indestructible.  That 
portion  of  the  visible  energy  that  is  apparently  destroyed  by 
friction  is  transformed  into  heat,  which  is  wasted,  so  far  as  the 
work  to  be  done  by  the  machine  is  concerned.  Let  I  represent 
internal  work  performed  in  the  machine,  i.e.,  the  wasted  work, 
and  W  w  the  external  work ;  then  our  general  formula  for 
machines,  as  modified  in  its  practical  applications,  becomes. 

(2)  Pp=Ww  +  I; 

that  is,  the  work  applied  to  a  machine  it  equal  to  the  effective 
work,  plus  the  internal  work  done  by  the  machine.     So  that,  so 


134  DYNAMICS. 

far  from  any  machine  being  a  source  of  power,  as  is  sometimes 
erroneously  supposed,  no  machine  practically  returns  as  much 
power  as  is  applied  to  it. 

By  division,  Formula  (1)  Pp  =  Ww  becomes 

^  f  -£; 

i.e.,  weight  :  power  :  :  the  distance  through  which  the  power 
>noves  :  the  distance  through  which  the  weight  is  moved  in  the 

same  time.    Prob- 

.  ... 

lems  pertaining  to 
machines  may  gen- 
erally be  solved  by 
Formula  (3),  and 
afterwards  suitable 
allowances  may  be 
made  for  the  in- 
ternal work  done. 
Thus,  suppose  that 
P  (Fig.  99)  is  10 
Ibs.,  and  it  is  re- 
quired to  find  what 
weight  (W)  it  will 
raise.  By  experi- 
ment we  find  that  P 
travels  8  ft.  while 
W  travels  4  ft. 
Then,  x  (W)  :  l6 
(P)  : :  8(p)  :  4(w)  ;  whence  x  =  20  Ibs.  The  20  Ibs.  in  W  is  just 
sufficient  to  balance  the  10  Ibs.  in  P ;  anything  less  than  20  Ibs. 
will  be  raised. 

It  is  to  be  observed  that,  as  we  saw  on  page  119,  work  is  not 
always,  or  even  usually,  expended  in  raising  a  weight,  but  in 
overcoming  resistance  of  any  kind  ;  so  we  may  interpret  Formula 
(3)  thus ;  resistance  :  power  :  :  the  distance  through  which  the 
power  moves  :  the  distance  through  which  the  resistance  is  over- 
come. 


QUESTIONS  AND  PROBLEMS. 


135 


QUESTIONS   AND    PROBLEMS. 

1.  If  the  power  applied  to  any  machine  is  2k,  and  it  moves  with  a 
velocity  of  10m  per  second,  wit^  what  velocity  can  it  move  a  resistance 
of  10k?   To  how  great  a  load  could  it  give  a  velocity  of  50m  per  second? 

2.  A  power  of  50k,  moving  through  a  space  of  100m,  is  capable  of 
moving  how  many  kilograms  through  a  space  of  2m?    What  advantage 
would  be  gained  by  the  use  of  the  machine  ? 

3.  Watch  the  movements  of  the  foot  in  working  the  treadle  of  a 
sewing-machine,  also  the  movements  of  the  needle  in  sewing,  and 
determine  what  mechanical  advantage  is  gained  by  the  machine. 

4.  Arrange  three  levers,  as  in  Figure  98;  and,  calling  the  distance 
(a&)  of  the  power  from  the  prop  the  power-arm  of  the  lever,  and  the 
distance  (be)  of  the  weight  from  the  prop  the  weight-arm,  verify  by 
experiment  the  following  special  formula  for  levers :  — 

•  W  _  £  _  power -arm 

P      w     weight-arm 

N.B.  —Equilibrium  must  first  be  established  between  the  two  arms  of  the  first 
lever,  by  placing  weights  on  the  short  arm. 

5.  Ascertain  the  advantage  that  may  be  gained  by  each  lever. 

1>.   A  lever  is  75cm  long ;  where  must  the  prop  be  placed  in  order  that 
a  power  of  2k  at  one  Fi    ^ 

end  may  move  4k  at 
the  other  end?  What 
will  be  the  pressure 
on  the  prop? 

7.  Show  that  the 
results    obtained    in 
the  last  problem  are 
consistent    with    the 
third  law  of  parallel 
forces  (page  95). 

8.  What  advantage 
is  gained  by  a  lever, 
when  its  power-arm 

is  longer  than  its  weight-arm?    What,  when  its  weight-arm  is  longer? 

9.  Two  weights,  of  5k  and  20k,  are  suspended  from  the  ends  of  a 
lever  70cm  long.    Where  must  the  prop  be  placed  that  they  may  balance? 

10.  What  mechanical  advantage  is  gained  by  a  lemon-squeezer? 

11.  If  P  (Fig.  99),  weighing  1  lb.,  is  suspended  15  spaces  from  the 
fulcrum  of  the  steelyard,  what  weight  (W)  suspended  3  similar  spaces 
the  other  side  of  the  fulcrum  will  balance  it? 


136 


DYNAMICS. 


12.  How  would  you  weigh  out  6  Ibs.  of  tea  with  the  same  steelyard? 

13.  If  the  circumference  of  the  axle,  Figure  100,  is  60cm,  and  the 
power  applied  to  the  crank  travels  240cm  during  each  revolution,  what 
power  will  be  necessary  to  raise  the  bucket  of  coal  weighing  (say)  40k? 

14.  How  many  meters  must  the  power  travel  (Fig.  100)  to  raise  the 
bucket  from  a  cavity  10m  deep? 

15.  (a)  In  the  train  of  wheels  (Fig.  101),  if  the  circumference  of 


Fig.  100. 


the  wheel  a  is  36  in.,  and  that 
of  the  pinion  &  is  4  in.,  a  power 
of  1  Ib.  at  P  will  exert  what 
force  on  the  circumference  of 
the  wheel  d  1  (&)  If  the  cir- 
cumference of  the  wheel  d  be 
30  in.,  and  that  of  the  pinion  c 
6  in.,  the  power  of  1  Ib.  at  P 
will  exert  what  force  on  the 
circumference  of  the  wheel/? 
(c)  If  the  circumference  of  the 
wheel /be  40  in.,  and  that  of  the  axle  e  8  in.,  how  many  pounds  in  W 
will  be  necessary  to  prevent  motion  of  the  train  of  wheels,  when  P 
Fig.  101.  weighs  1  Ib.?  (d)  If  W  has  a 

velocity  of  5  ft.  per  second, 
what  will  be  P's  velocity? 

16.  Prepare  a  special   for- 
mula for  the  solution  of  prob- 
lems pertaining  to  the  wheel 
and  axle. 

17.  The     weight    W    (Fig. 
102),   in    traversing    the    in- 
clined   plane   AB,   only   rises 
through  the  vertical  hight  CB, 
while  P  must  move  through  a 
distance  equal  to  AB.      Let 
L  represent  the  length  of  an 
inclined  plane,  and  H  its  hight, 
and  prepare  a  special  formula 

for  the  solution  of  problems  pertaining  to  the  inclined  plane. 

18.  A  skid  12  ft.  long  rests  one  end  on  a  cart  3  ft.  high,  and  the 
other  end  on  the  ground.    What  force  must  a  boy  exert  while  rolling  a 
barrel  of  flour  weighing  200  Ibs.  over  the  skid  into  the  cart? 

19.  During  one  revolution  a  screw  advances  a  distance  equal  to  the 


QUESTIONS   AND   PROBLEMS. 


13T 


distance  between  two  turns  of  the  thread,  measured  in  the  direction  of 
the  axis  of  the  screw.  Suppose  the  screw  in  the  letter-press,  Figure 
103,  to  advance  £  in.  at  each  revolution,  and  a  power  of  25  Ibs.  to  be 
applied  to  the  circumference  of  the  wheel  6,  whose  diameter  is  14  in. 
What  pressure  would  be  ex- 
erted on  articles  placed  be- 
neath the  screw.  [The  cir- 
cumference of  a  circle  is 
3.1416  times  its  diameter.] 
20.  The  toggle-joint  (Fig. 
104)  is  a  machine  employed 
where  great  pressure  has  to 
be  exerted  through  a  small 
space,  as  in  punching  and 
shearing  iron,  and  in  print- 
ing-presses, in  pressing  the  types  forcibly  against  the  paper.  An 


Fig.  103. 


illustration  may  be  found  in  the 
joints  used  to  raise  carriage-tops. 
Force  applied  to  the       Fig  104 
joint    c    will    cause 
the  two  links  ac  and 
be   to    be    straight- 
ened, or  carried  for- 
ward to  d,  while  the 
guides  move  through 
a  distance  equal  to 
(ac  +  6c)  —  ab.      If 
dc  =  10cm,  ab  =  98cm, 
and  ac  +  be  —  100cm, 
then  a  force  of  80s  applied  at  c  would  exert  what  average  pressure 
on  obstacles  in  the  path  of  the  guides? 

21.    Show  that  the  hydrostatic  press,  page  65,  conforms  in  its  oper- 
ation to  the  general  law  of  machines. 


CHAPTER    III. 

MOLECULAR   ENERGY.  -  HEAT. 


XVII.     WHAT   HEAT   IS.  — SOME    SOURCES    OF   HEAT. 

IN  the  preceding  pages  the  theory  of  heat  has  been  several 
times  anticipated ;  we  are  now  better  qualified  to  judge  of  its 
truth  or  falsity. 

§  102.  Mechanical  motion  convertible  into  heat.  —  Ex- 
periments. Hold  some  small  steel  tool  upon  a  rapidly  revolving  dry 
grindstone;  a  shower  of  sparks  flies  from  the  stone.  Place  a  ten- 
penny  nail  upon  a  stone  and  hammer  it  briskly ;  it  soon  becomes  too 
hot  to  be  handled  with  comfort,  and  we  may  conceive  that  if  the 
blows  were  rapid  and  heavy  enough,  it  might  soon  become  red  hot. 
Rub  a  desk  with  your  fist,  and  your  coat-sleeve  with  a  metallic  but- 
ton ;  both  the  rubbers  and  the  things  rubbed  become  heated. 

You  observe  that  in  every  case  heat  is  generated  at  the  ex- 
pense of  work  or  mechanical  motion,  i.e.,  mechanical  motion 
checked  becomes  heat.  When  the  brakes  are  applied  to  the 
wheels  of  a  rapidly  moving  railroad  train,  its  motion  is  all  con- 
verted into  heat,  much  of  which  may  be  found  in  the  wheels, 
brake-blocks,  and  rails.  The  meteorites,  or  "shooting-stars," 
which  are  seen  at  night  passing  through  the  upper  air,  some- 
times strike  the  earth,  and  are  found  to  be  stones  heated  to  a 
light-giving  state.  They  become  heated  when  they  reach  our 
atmosphere,  in  consequence  of  their  motion  being  checked  by 
the  resistance  of  the  air. 

§  103.  Heat  convertible  into  mechanical  motion.  — 
Experiment.  Take  a  thin  glass  flask  A,  Figure  105,  and  half  fill  it 
with  water;  fit  a  cork  air-tight1  in  its  neck.  Perforate  the  cork, 

1  A  good  way  to  make  a  cork  air-tight  is  to  soak  it  in  melted  paraffine. 


HEAT  DEFINED. 


139 


.  105. 


insert  a  glass  tube  bent  as  indicated  in  the  figure,  and  extend  it  into 
the  water.  Apply  heat  to  the  flask ;  soon  the  liquid  rises  in  the  tube, 
and  flows  from  its  upper  end. 

Here  heat  produces  mechanical  motion,  and  does  work  in  rais- 
ing a  weight  in  opposition  to  gravity.  Every  steam  engine  is  a 
heat  engine.  All  the  power  of  steam  consists 
in  its  heat.  The  steam  which  leaves  the  C3*lin- 
der  of  an  engine  (see  page  176),  after  it  has 
set  the  piston  in  motion,  is  cooler  than  when 
it  entered,  and  cooler  in  proportion  to  the  work 
done.  Furthermore,  it  will  be  shown  (page  174) 
that  heat  and  work  are  so  related  to  each  other 
that  a  definite  quantity  of  the  one  is  always  equal 
to  a  definite  quantity  of  the  other. 

Now,  when  the  appearance  of  one  thing  is  so 
connected  with  the  disappearance  of  another, 
that  the  quantity  of  the  thing  produced  can  be 
calculated  from  the  quantity  of  that  which  dis- 
appears, we  conclude  that  the  one  has  been 
formed  at  the  expense  of  the  other,  and  that 
the}7  are  only  diferent  forms  of  the  same  thing. 
We  have,  therefore,  reason  to  believe  that  heat  is  of  the  same 
nature  as  mechanical  energy,  i.e.,  it  is  only  another  form  of 
kinetic  energy. 

§  104.  Heat  defined. — A  body  loses  motion  in  communi- 
cating it  (page  88) .  The  hammer  descends  and  strikes  the  an- 
vil ;  its  motion  ceases,  but  the  anvil  is  not  sensibly  moved ; 
the  only  observable  effect  produced  is  heat.  Instead  of  the  pro- 
gressive motion  of  the  hammer  as  a  whole,  there  is  now,  accord- 
ing to  the  modern  view,  an  increased  vibratory  motion  of  the 
molecules  that  compose  the  hammer,  —  a  mere  change  of  motion 
in  kind  and  locality.  Of  course,  this  latter  motion  is  invisible. 
The  conclusion  is  that  heat  is  molecular  motion.  A  body  is  heated 
by  having  the  motion  of  its  molecules  quickened,  and  cooled  by 


140  MOLECULAR   ENERGY.  —  HEAT. 

parting  with  some  of  its  molecular  motion.  One  body  is  hotter 
than  another  when  the  average  energy  of  each  molecule  in  it  is 
greater  than  in  the  other. 

§  105.  Heat  generated  by  chemical  action.  —  Experi- 
ment. Take  a  glass  test-tube  half  full  of  cold  water,  and  pour  into  it 
one-fourth  its  volume  of  sulphuric  acid.  The  liquid  almost  instantly 
becomes  so  hot  that  the  tube  cannot  be  held  in  the  hand. 

When  water  is  poured  upon  quicklime  heat  is  rapidly  devel- 
oped. The  invisible  oxygen  of  the  air  combines  with  the  vari- 
ous fuels,  such  as  wood,  coal,  oils,  and  illuminating  gas,  and 
gives  rise  to  what  we  call  burning  or  combustion,  by  which  a 
large  amount  of  heat  is  generated.  In  all  such  cases  the  heat 
is  generated  by  the  combination  or  clashing  together  of  mole- 
cules of  substances  that  have  an  affinity  (i.e.,  an  attraction) 
for  each  other.  Before  their  union  they  are  in  the  condition 
of  a  weight  drawn  up ;  while  approaching  each  other,  they  are 
like  the  falling  weight;  and  when  they  collide,  their  motion, 
like  that  of  the  weight  when  it  strikes  the  earth,  is  converted 
into  heat.  The  chemical  potential  energy  of  the  molecules  is 
converted,  in  the  act  of  combination,  into  kinetic  energy,  —  into 
molecular  motion. 

§  106.  Origin  of  animal  heat  and  muscular  motion.  — 
The  plant  finds  its  food  in  the  air  (principally  the  carbonic  acid 
in  the  air)  and  in  the  earth  in  the  condition  of  a  fallen  weight ; 
but,  by  the  agency  of  the  sun's  radiation,  work  is  performed  upon 
this  matter  during  the  growth  of  the  plant ;  potential  energy  is 
stored  in  the  plant,  —  the  weight  is  drawn  up.  The  animal  now 
finds  its  food  in  the  plant,  appropriates  the  energy  stored  in 
the  plant,  and  converts  it  into  energy  of  motion  in  the  form  of 
heat  and  muscular  motion.  The  plant,  then,  may  be  regarded 
as  a  machine  for  converting  energy  of  motion  received  from  the 
sun  into  potential  energy ;  the  animal,  as  a  machine  for  trans- 
forming it  again  into  the  energy  of  motion. 


TEMPERATURE  DEFINED.  141 

§  107.  The  sun  as  a  source  of  energy.  —  Not  only  is  the 
sun  the  source  of  the  energy  exhibited  in  the  growth  of  plants, 
as  well  as  of  the  muscular  and  heat  energy  of  the  animal,  but  it 
is  the  source,  directly  or  indirectly,  of  very  nearly  all  the  energy 
employed  by  man  in  doing  work.  Our  coal-beds,  the  results  of 
the  deposit  of  vegetable  matter,  are  vast  storehouses  of  the  sun's 
energy,  rendered  potential  during  the  growth  of  the  plants  many 
ages  ago.  Every  drop  of  water  that  falls  to  the  earth,  and  rolls 
its  way  to  the  sea,  contributing  its  mite  to  the  unbounded  water- 
power  of  the  earth,  and  every  wind  that  blows,  derives  its  power 
directly  from  the  sun. 

XVIII.     TEMPERATURE. 

§  108.  Temperature  denned.  —  If  body  A  is  brought  in 
contact  with  body  B,  and  A  loses  and  B  gains  in  heat,  then  A  is 
said  to  have  had  originally  a  higher  temperature  than  B.  If 
neither  body  gains  or  loses,  then  both  had  the  same  tempera- 
ture. Temperature  is  the  state  of  a  body  with  reference  to  its 
power  of  communicating  heat  to  or  receiving  heat  from  other 
bodies.  The  direction  of  the  flow  of  heat  determines  which  of 
two  bodies  has  the  higher  temperature. 

§  109.  Temperature  distinguished  from  quantity  of 
heat.  —  The  term  temperature  has  no  reference  to  quantity  of 
heat.  If  we  mix  together  two  equal  quantities  of  a  substance  at 
the  same  temperature,  the  temperature  of  the  mixture  is  not  the 
sum  of  the  temperatures,  —  it  is  not  greater  or  less  than  either 
before  they  were  mixed  ;  but  evidently  the  mixture  contains 
twice  as  much  heat  as  either  alone.  If  we  dip  from  a  gallon  of 
boiling  water  a  cupful,  the  cup  of  water  is  just  as  hot,  i.e., 
has  the  same  temperature,  as  the  larger  quantity,  although  of 
course  there  is  a  great  difference  in  the  quantities  of  heat  the 
two  bodies  of  water  contain.  Temperature  depends  upon  the 
average  kinetic  energy  of  the  individual  molecule,  while  quantity 
of  heat  depends  upon  the  average  kinetic  energy  of  the  individual 
molecule  multiplied  by  the  number  of  molecules. 


142  MOLECULAR  ENERGY.  —  HEAT. 


XIX.     DIFFUSION    OF    HEAT. 

There  is  always  a  tendency  to  equalization  of  temperature; 
that  Is,  heat  has  a  tendency  to  pass  from  a  warmer  body  to  a 
colder,  or  from  a  warmer  to  a  colder  part  of  the  same  body, 
until  there  is  an  equilibrium  of  temperature. 


§  110.  Conduction.  —  Experiment  1.  Place  one  end  of  a  wire 
about  15cm  long,  in  a  lamp-flame,  and  hold  the  other  end  in  the  hand. 
Heat  gradually  travels  from  the  end  in  the  flame  toward  the  hand. 
Apply  your  fingers  successively  at  different  points  nearer  and  nearer 
the  flame ;  you  find  that  the  nearer  you  approach  the  flame  the  hotter 
the  wire  is. 

The  flow  of  heat  through  an  unequally-heated  body,  from 
places  of  higher  to  places  of  lower  temperature,  is  called  con- 
duction ;  the  body  through  which  it  travels  is  called  a  conductor. 
The  molecules  of  the  wire  in  the  flame  have  their  motion  quick- 
ened ;  they  strike  their  neighbors  and  quicken  their  motion  ;  the 
latter  in  turn  quicken  the  motion  of  the  next ;  and  so  on,  until 
some  of  the  motion  may  be  finally  communicated  to  the  hand, 
and  creates  in  it  the  sensation  of  heat. 

Experiment  2.  Hold  wires  of  different  metals  of  the  same  length, 
also  a  glass  tube,  a  pipe-stem,  etc.,  in  the  flame,  and  notice  the  differ- 
ence in  time  that  elapses  before  the  sensation  of  heat  is  felt  in  the 
different  bodies. 

Experiment  3.  Go  into  a  cold  room,  and  place  the  bulb  of  a  ther- 
mometer in  contact  with  various  substances  in  the  room ;  you  will 
probably  find  that  they  have  the  same,  or  very  nearly  the  same,  tem- 
perature. Place  your  hand  on  the  same  substances ;  they  appear  to 
have  very  different  temperatures.  This  is  due  to  the  fact  that  some 
substances  conduct  heat  away  from  the  hand  faster  than  others.  Those 
substances  that  appear  coldest  are  the  best  conductors.  If  you  go  into 
a  room  warmer  than  your  body,  all  this  is  reversed  ;  those  substances 
which  feel  warmest  are  the  best  conductor,?,  because  they  conduct  their 
own  heat  to  your  hand  fastest. 

Experiment  4.  Twist  together  at  one  end  similar  wires  or  strips 
of  iron,  copper,  brass,  etc.,  10  or  15cm  long,  and  introduce  them  into  a 


CONVECTION.  143 

small  flame.  After  a  few  minutes  you  can  tell  approximately  the  order 
of  their  conducting  powers,  by  moving  a  match  along  each  wire,  and 
seeing  how  far  from  the  flame  it  will  light. 

You  learn  that  some  substances  conduct  heat  much  more 
rapidly  than  others.  The  former  are  called  good  conductors, 
the  latter  poor  conductors.  Metals  are  the  best  conductors, 
though  they  differ  widely  among  themselves. 

Experiment  5.  Fill  a  test-tube  nearly  full  of  water,  and  hold  it 
somewhat  inclined  (Fig.  106),  so  that  a  flame  may  heat  the  part  of  the 
tube  near  the  surface  of  the  water.  The  Fi 

water  may  be  made  to  boil  near  its  surface 
for  several  minutes  before  any  change  of 
the  temperature  at  the  bottom  will  be  per- 
ceived. 


Liquids,  as  a  class,  are  poorer  con- 
ductors than  solids.  Gases  are  much 
poorer  conductors  than  liquids.  It  is 
difficult  to  discover  that  pure,  dry  air 
possesses  any  conducting  power.  The 
poor  conducting  power  of  our  clothing  is  due  to  the  poor  con- 
ducting power  of  the  fibres  of  the  cloth  in  part,  but  chiefly  to 
the  air  which  is  confined  by  it.  (Why  is  loose  clothing  warmer 
than  that  closely  fitting  ?) 

Bodies  are  surrounded  with  bad  conductors,  to  retain  heat 
when  their  temperature  is  above  that  of  surrounding  objects, 
and  to  exclude  it  when  their  temperature  is  below  that  of  sur- 
rounding objects. 

§  111.  Convection.  —  When  a  hot  brick,  or  a  bottle  of  hot 
water,  is  placed  at  one's  feet,  heat  is  also  conveyed  to  the  feet. 
When  heat  is  transferred  from  one  place  to  another  by  the 
bodily  moving  of  heated  substances,  the  operation  is  called 
convection;  but  this  term  is  rarely  applied  to  solids.  Solids 
require  some  external  force  to  effect  the  conveyance ;  fluids  do 
not  necessarily,  as  may  be  seen  by  the  following  experiments  :  — 


144 


MOLECULAR  ENERGY.  —  HEAT. 


Experiment  1.  Arrange  apparatus  as  in  Fig.  107.  Fill  the  large 
beaker  nearly  full  of  water,  and  elevate  it  so  that  the  tip  of  a  Bunsen 
flame  may  just  touch  the  middle  of  the  bottom.  Fill  a  glass  tube  B 


Fig.  107. 


Fig.  108. 


with  a  deeply-colored  aniline  solution,  stop  one  end 
with  a  finger,  and  thrust  the  other  end  into  the  water 
to  the  bottom  of  the  beaker ;  remove  the  finger,  and 
allow  the  solution  to  flow  out  and  color  the  water  at 
the  bottom  for  a  little  depth.  Soon  the  colored 
liquid  immediately  over  the  flame  becomes  heated, 
expands,  and  thereby  becomes  less  dense  than  the 
liquid  above ;  consequently  it  risves  and  forms  an  up- 
ward current  through  the  colorless  liquid.  At  the 
same  time  the  cooler  liquid^on  the  sides  descends  to 
take  the  place  of  that  which  rises,  and  soon  the 
descending  currents  become  visible  by  the  coloration 
of  the  water.  By  this  means  heat  is  conveyed  to  all 
parts  of  the  liquid,  which  would  otherwise  become 
much  hotter  at  the  bottom  than  at  the  top  in  conse- 
quence of  the  poor  conducting  power  of  water. 

If  a  glass  tube  C,  bent  as  shown  in  the  figure,  is 
filled  with  water,  and  introduced  into  the  beaker  so 
that  the  orifice  of  the  short  arm  shall  be 
just  beneath  the  surface  of  the  colored 
water,  the  colored  liquid  will  be  seen  slowly 
to  ascend  the  short  arm,  while  the  colder 
water  will  descend  the  longer  arm. 

Experiment  2.  Provide  a  tightly-cov- 
ered tin  vessel  (Fig.  108)  and  two  lamp- 
chimneys  A  and  B.  Near  one  side  of  the 
top  of  the  cover  cut  a  hole  a  little  smaller 
than  the  large  aperture  of  chimney  B.  Near 
the  opposite  side  of  the  cover  cut  a  series  of 
holes  of  about  7mm  diameter,  arranged  in  a 
circle,  the  circle  being  large  enough  to  ad- 
mit a  candle  without  covering  the  holes. 
Light  the  candle,  and  cover  it  with  chim- 
ney A,  which  should  be  outside  the  circle 
of  holes.  Fasten  both  chimneys  to  the 
cover  with  wax.  Hold  smoking  touch-paper  C  (see  page  278)  near  the 
top  of  chimney  B.  The  smoke,  instead  of  rising,  as  it  usually  does, 
rapidly  descends  the  chimney,  and  in  a  few  seconds  will  be  found 


VENTILATION.  145 

ascending  chimney  A.  The  air  around  the  flame  becomes  heated,  ex- 
pands, and  rises,  while  air  from  the  outside  rushes  down  the  other 
chimney  to  supply  the  deficiency  in  the  rarefied  space.  Thus  heat 
from  the  flame  is  conveyed  away  to  distant  places.  Cover  the  orifice 
of  chimney  B  with  the  hand,  and  the  flame  will  quickly  go  out. 

The  last  experiment  furnishes  an  explanation  of  many 
familiar  phenomena.  It  explains  the  cause  of  chimney  drafts, 
and  shows  the  necessity  of  providing  a  means  of  ingress  as  well 
as  egress  of  air  to  and  from  a  confined  fire.  It  explains  the 
method  by  which  air  is  put  in  motion  in  winds.  It  illustrates  a 
method  often  adopted  to  ventilate  mines.  Let  the  interior  of  the 
tin  vessel  represent  a  mine  deep  in  the  earth,  and  the  chimneys 
two  shafts  sunk  to  opposite  extremities  of  the  mine.  A  fire 
kept  burning  at  the  bottom  of  one  shaft  will  cause  a  current  of 
air  to  sweep  down  the  other  shaft,  and  through  the  mine,  and 
thus  keep  up  a  circulation  of  pure  air  through  the  mine. 

Liquids  and  gases  are  heated  by  convection.  ( Wiry  not  solids  ?) 
The  heat  must  be  applied  at  the  bottom  of  the  body  of  liquid  or 
gas.  (Why  not  at  the  top?)  There  is  a  still  more  important 
method  by  which  heat  is  diffused,  called  radiation,  which  will  be 
treated  of  in  its  proper  place,  under  the  head  of  radiant  energy. 

§  112.  Ventilation.  —  Intimately  connected  with  the  topic 
Convection,  is  the  subject  (of  vital  importance)  Ventilation,  inas- 
much as  our  chief  means  of  securing  the  latter  is  through  the 
agency  of  the  former.  The  chief  constituents,  of  our  atmosphere 
are  nitrogen  and  oxygen,  with  varying  quantities  of  water  vapor, 
carbonic  acid  gas,  ammonia  gas,  nitric  acid  vapor,  and  other 
gases.  The  atmosphere  also  contains  in  a  state  of  suspension 
varying  quantities  of  small  particles  of  free  carbon  in  the  form  of 
smoke,  microscopic  organisms,  and  dust  of  innumerable  sub- 
stances. All  of  these  constituents  except  the  first  three  are 
called  impurities.  Carbonic  acid  is  the  impurity  that  is  usually 
the  most  abundant  and  most  easily  detected ;  so  it  has  come  to 
be  taken  as  the  measure  of  the  purity  of  the  atmosphere,  though 


146 


MOLECULAR  ENERGY.  —  HEAT. 


not  itself  the  most  deleterious  constituent.  Pure  out-door  air 
contains  about  4  parts  of  it  by  volume  in  10,000.  If  the  quan- 
tity rises  to  10  parts,  the  air  becomes  unwholesome. 

Experiment  1.  Place  a  teaspoonful  of  unslacked  lime  ill  a  tumbler 
of  water ;  a  part  of  it  will  be  dissolved.  Filter  the  solution  through 
unsized  paper,  and  into  the  clear  liquid  blow  breath  from  the  lungs 
through  a  glass  tube.  The  liquid  turns  milky-white  in  appearauce, 
because  the  carbonic  acid  in  the  breath  unites  with  the  lime  dissolved 
in  the  water,  and  forms  the  insoluble  carbonate  of  lime,  which  remains 
suspended  for  a  time  in  the  liquid,  but  finally  settles  as  a  white  powder 
at  the  bottom. 

Experiment  2.    Take  a  fresh  quantity  of  lime  water  in  each  of  two 
Fig  109.  glasses,  and  in  any  poorly-ventilated  room  which  has 

been  occupied  by  several  persons  for  a  short  time 
(unfortunately  almost  any  school-room  will  answer 
the  purpose),  place  one  glass  near  the  floor,  and  with 
a  bellows  blow  into  the  liquid  a  few  puffs  of  the  lower 
stratum  of  air.  Then  place  the  other  glass  near  the 
top  of  the  room,  and  blow  with  the  bellows  some  of 
the  upper  stratum  of  air  into  the  lime  water.  In  both 
cases  carbonic  acid  will  be  found  to  be  present,  but 
it  will  be  much  more  abundant  in  the  upper  stratum, 
us  shown  by  the  greater  rapidity  with  which  the 
cloudiness  is  produced  in  the  upper  stratum. 

Experiment  3.  In  the  center  of  a  small  circular 
plauk  (Fig.  109)  insert  an  iron  wire  60cm  long  and 
jmm  in  diameter.  At  intervals  of  9cm  solder  to  the 
wire  short  pieces  of  small  wire,  so  as  to  project 
horizontally  from  the  large  wire ;  and  to  the  free  ex- 
tremities of  these  short  wires  solder  small  circular 
pieces  of  tin  3cm  in  diameter.  Arrange  these  little 
platforms  spirally  around  the  vertical  wire.  Fix 
stumps  of  candles  upon  these  platforms  by  means  of 
a  little  melted  tallow.  Light  the  candles,  and  carefully 
cover  the  whole  with  a  tall  glass  jar.  Heated  air, 
from  which  the  life-sustaining  oxygen  has  been  largely  extracted 
and  replaced  by  carbonic  acid,  rises  from  each  flame  and  accumulates 
at  the  top  of  the  jar.  This  air  will  neither  support  life  nor  combus 
tion,  consequently  the  highest  candle  flame  is  quickly  extinguished. 
The  colder  and  purer  air  descends  and  feeds  the  lower  flames,  while 


VENTILATION.  147 

flame  after  flame,  from  the  top  downward,  is  successively  extinguished, 
the  lowest  flame  being  the  last  to  go  out. 

Carbonic  acid  gas  is  about  one  and  one-half  times  heavier 
than  air  at  the  same  temperature  ;  consequently,  when  both  have 
the  same  temperature,  and  the  former  is  very  abundant,  it  tends 
to  settle  to  the  bottom,  as  in  the  vicinity  of  lime-kilns,  in  which 
large  quantities  of  this  gas  are  generated. 

The  knowledge  of  this  fact  has  led  many  to  suppose  that  a 
means  for  the  escape  of  impure  air  need  only  be  provided  near 
the  floor  of  a  room.  But  it  should  be  remembered  (1)  that  the 
tendency  of  carbonic  acid  gas,  unless  present  in  excessive  quan- 
tities, is  to  diffuse  itself  equally  through  a  body  of  air ;  but  (2) 
when  it  is  heated  to  a  temperature  above  that  of  the  surrounding 
air,  as  when  generated  by  flames,  or  when  it  escapes  in  the  warm 
breath  of  animals,  it  is  lighter  than  the  air,  and  consequently  rises. 
If  this  impure  air  could  escape  at  the  ceiling  while  fresh  air  en- 
tered at  the  floor,  the  ventilation  would  be  good.  But  usually  this 
fresh  air  must  be  warmed  ;  and  in  passing  over  a  stove,  furnace, 
or  steam  radiator,  its  temperature  will  generally  become  higher 
than  that  of  the  impure  air,  so  that  it  will  rise  above  the  latter, 
and  pass  out  at  a  ventilator  in  the  ceiling,  leaving  the  floor  cold  ; 
hence,  the  most  impure  air  is  often  found  in  high  school-rooms 
half-way  up. 

Experience  shows  that,  with  the  ordinary  means  of  heating,  it 
is  usually  best,  in  cold  weather,  to  provide  for  the  escape  of  the 
foul  air  at  the  floor  into  a  flue,  in  which  a  'draft  is  maintained 
by  a  neighboring  hot  chimney-flue,  or  a  gas-burner,  while  the 
warm,  fresh  air  is  introduced  at  the  floor,  on  the  opposite  side 
of  the  room,  or  sometimes  at  the  ceiling. 

The  quantity  of  fresh  air  introduced  must  be  great  enough  to 
dilute  the  impurities  till  they  are  harmless.  An  adult  makes 
about  18  respirations  per  minute,  expelling  from  his  lungs  at 
each  inspiration  about  500ccm  of  air,  over  4  per  cent  of  which  is 
carbonic  acid.  At  this  rate,  about  9,000ccm  of  air  per  minute 
become  unfit  for  respiration  ;  and  to  dilute  this  sufficiently,  good 


148  MOLECULAR   ENERGY.  —  HEAT. 

authorities  say  that  about  100  times  as  much  fresh  air  is  needed  ; 
or,  for  proper  ventilation,  about  a  cubic  meter  of  fresh  air  per 
minute  is  needed  for  each  person,  or,  in  English  measures,  2,000 
cubic  feet  per  hour.  ' 

If  the  heating  could  be  so  arranged  as  to  keep  the  floor  prop- 
erly warmed,  the  vitiated  air  might  pass  out  at  the  ceiling,  and 
the  quantity  of  fresh  air  entering  at  the  floor  might  be  mftch 
less  than  that  just  stated.  In  mild  weather,  when  the  fresh  air 
does  not  require  warming,  the  inlet  may  be  at  the  floor  and  the 
outlet  at  the  ceiling. 

QUESTIONS  AND    PROBLEMS. 

1.  How  would  you  ventilate  the  tall  jar  in  Experiment  3  ? 

2.  At  evening  assemblies  in  lighted  halls,  what  two  fruitful  sources 
of  carbonic  acid  are  ever  present  ? 

3.  Why  are  gas  burners  frequently  placed  under  the  orifices  of  ven- 
tilators ? 

4.  A  bed  room  is  3m  square  and  2.5m  high ;  how  long  would  the  en- 
closed air  supply  two  persons  on  the  supposition  that  none  was  to  be 
re-breathed  ? 

5.  A  hall  contains  a  thousand  persons,  and  its  dimensions  are  35  X 
18  X  7m.     How  often  should  a  complete  change  of  air  be  effected  that  it 
may  not  become  vitiated  ? 

XX.     EFFECTS   OF  HEAT.  —  EXPANSION. 

Having  learned  something  of  the  nature  of  heat,  and  how  it 
passes  from  point  to  point,  let  us  examine  the  effects  it  pro- 
duces on  bodies :  these  are  expansion  and  change  of  state. 
The  first  gives  a  means  of  measuring  temperature,  and  leads  to 
a  fuller  stud}'  of  gases  than  we  have  yet  made.  Under  the 
second  effect  of  heat  we  study  liquefaction  and  vaporization.  A 
third  effect  that  is  very  obvious,  the  change  of  temperature,  will  be 
found  to  depend  in  part  on  what  is  called  specific  heat,  to  be 
studied  on  page  170. 

§  113.  Expansion  of  solids,  liquids,  and  gases.  —  Ex- 
periment 1.  Obtain  two  short  brass  tubes,  —  one  of  a  size  that  will 


COEFFICIENTS   OF   EXPANSION. 


149 


Fig.  110. 


permit  it  just  to  enter  the  bore  of  the  other.     Heat  the  smaller  tube ; 
it  will  no  longer  enter  the  larger. 

Experiment  2.  Fit  stoppers  tightly  in  the  necks  of  two  similar  thin 
glass  flasks  (or  test-tubes),  and  through  each  stopper  pass  a  glass  tube 
about  60cm  long.  The  flasks  must  be  as  nearly  alike  as  possible.  Fill  one 
flask  with  alcohol  and  the  other  with  water,  and  crowd  in  the  stoppers 
so  as  to  force  the  liquids  in  the  tubes  a  little  way  above  the  corks. 
Set  the  two  flasks  into  a  basin  of  hot  water,  and  note  that,  at  the 
instant  the  flasks  enter  the  hot  water,  the  liquids  sink  a  little  in  the 
tubes,  but  quickly  begin  to  rise,  until  perhaps  they  reach  the  top  of  the 
tubes  and  run  over. 

When  the  flasks  first  enter  the  hot  water  they  expand,  and  thereby 
their  capacities  are  increased ;  meantime  the  heat  has  not  reached  the 
liquids  to  cause  them  to  expand,  consequently  the  liquids  sink  momen- 
tarily to  accommodate  themselves  to  the  enlarged  vessel.  Soon  the 
heat  reaches  the  liquids,  and  they  begin  to  expand,  as  shown  by  their 
rise  in  the  tubes.  The  alcohol  rises  faster  than 
the  water.  Different  substances,  both  in  the  solid 
and  liquid  states,  expand  unequally  on  experi- 
encing equal  changes  of  temperature. 

Experiment  3.  Take  one  of  the  flasks  used 
in  the  last  experiment,  dry  it  well  inside  and  out- 
side, invert  the  flask,  insert  the  end  of  the  tube 
in  a  bottle  of  colored  water  (Fig.  110),  and  apply 
heat  to  the  flask ;  the  enclosed  air  expands  and 
comes  out  through  the  colored  liquid  in  bubbles. 
After  a  few  minutes,  withdraw  the  heat,  keeping 
the  end  of  the  tube  in  the  liquid ;  as  the  air  left 
in  the  flask  cools,  it  contracts,  and  the  water  is 
forced  by  atmospheric  pressure  up  the  tube  into 
the  flask,  and  partially  fills  it. 

§  114.  Coefficients  of  expansion.— There 
being  generally  greater  cohesive  force  between  the  molecules  of 
solids  than  between  the  molecules  of  liquids,  the  former  expand 
less  than  the  latter  on  receiving  the  same  amount  of  heat,  and 
for  the  same  reason  liquids  expand  less  than  gases.  (See  page 
18.)  All  gases  expand  alike  for  equal  differences  of  tempera- 
ture, and  the  expansion  is  uniform  at  all  temperatures.  Under 
uniform  pressure  the  volume  of  any  body  of  gas  is  increased  by 


150  MOLECULAR   ENERGY.  —  HEAT. 

2^3-  its  volume  at  the  freezing  point  of  water  for  every  degree  cen- 
tigrade, or  ¥£T  for  every  degree  Fahrenheit,  its  temperature  is 
raised.  These  fractions  are  called  the  coefficients  of  expansion. 
Not  only  do  the  coefficients  of  expansion  of  liquids  and  solids 
vary  with  the  substance,  but  the  coefficient  for  the  same  sub- 
stance varies  at  different  temperatures,  being  greater  at  high 
than  at  low  temperatures. 

In  the  expansion  of  fluids  we  have  only  to  do  with  increase  of 
volume,  called  cubical  expansion.  In  the  expansion  of  solids, 
we  have  frequent  occasion  to  speak  of  expansion  in  one  direc- 
tion onty,  and  this  is  called  linear  expansion. 

§  115.  Power  of  expansion  and  contraction.  —  The  force 
which  may  be  exerted  by  bodies  in  expanding  or  contracting  may  be 
very  great,  as  shown  by  the  following  rough  calculation :  If  an  iron 
bar,  1  sq.  in.  in  section,  is  raised  from  0°  C.  (freezing  point  of  water)  to 
500°  C.  (a  dull,  red  heat),  its  length,  if  allowed  to  expand  freely,  will  be  in- 
creased from  1  to  1.006,  its  coefficient  of  expansion  being  about  .000012. 
Now,  a  force  capable  of  stretching  a  bar  of  iron  of  1  sq.  in.  section 
this  amount,  is  about  90  tons,  which  represents  very  nearly  the  force 
that  would  be  necessary  to  prevent  the  expansion  caused  by  heat.  It 
would  require  an  equal  force  to  prevent  the  same  amount  of  contrac- 
tion (caused  by  what?)  if  the  bar  is  cooled  from  500°  to  0°  C.  -  * 

Boiler  plates  are  riveted  with  red-hot  rivets,  which,  on  cooling, 
draw  the  plates  together  so  as  to  form  very  tight  joints.  Tires  are 
fitted  on  carriage-wheels  when  red  hot,  and,  on  cooling,  grip  them  with 
very  great  force. 

§  116.  Abnormal  expansion  and  contraction  of  water. 
—  Water  presents  a  partial  exception  to  the  general  rule  thnl 
matter  expands  on  receiving  heat  and  contracts  on  losing  it 
If  a  quantity  of  water  at  0°  C.,  or  32°  F.,  is  heated,  ii 
contracts  as  its  temperature  rises,  until  it  reaches  4°  C.,  or 
about  39°  F. ,  when  its  volume  is  least,  and  therefore  it  has  its 
maximum  density.  If  heated  beyond  this  temperature  it  ex- 
pands, and  at  about  8°  C.  its  volume  is  the  same  as  at  G°.  On 
cooling,  water  reaches  its  maximum  density  at  4°  C.,  and  ex- 
pands as  the  temperature  falls  below  that  point.  It  is  probable 


THERMOMETRY.  151 

tnat  cr3Tstallization,  and  consequently  expansion  (see  page  26), 
begins  at  4°  C.  (What  is  the  temperature  at  the  bottom  of  a 
pond  when  water  begins  to  freeze  at  the  surface  ?) 

XXI.     THERMOMETRY. 

§  117.  Temperature  measured  by  expansion.  —  The  ef- 
fects of  expansion  b}7  heat  are  well  illustrated  in  the  common 
thermometer.  As  its  temperature  rises,  both  the  glass  and  the 
mercury  expand ;  but,  as  liquids  are  more  expansible  than 
solids,  the  mercury  expands  much  more  rapidly  than  the  glass, 
and  the  apparent  expansion  of  the  mercury,  shown  by  its  rise  in 
the  tube,  is  the  difference  between  the  actual  increase  of  volume 
of  the  mercury  and  that  of  the  part  of  the  glass  vessel  containing 
it.  The  thermometer,  then,  primarily  indicates  changes  in  vol- 
ume ;  but  as  changes  of  volume  in  this  case  are  caused  by 
changes  of  temperature,  it  is  commonly  used  for  the  more 
important  purpose  of  measuring  temperature.  (Will  a  ther- 
mometer measure  quantity  of  heat?) 

§  118.  Construction  of  a  thermometer.  —  A  thermometer 
generally  consists  of  a  glass  tube  of  capillary  bore,  terminating 
at  one  end  in  a  bulb.  The  bulb  and  part  of  the  tube  are  filled 
with  mercury,  and  the  space  in  the  tube  above  the  mercury  is 
usually,  but  not  necessarily,  a  vacuum.  On  the  tube,  or  on  a 
plate  of  metal  behind  the  tube,  is  a  scale,  to  show  the  hight  of 
the  mercurial  column. 

§  119.  Standard  temperatures.  —  That  a  thermometer 
may  indicate  any  definite  temperature,  it  is  necessary  that  its 
scale  should  relate  to  some  definite  and  unchangeable  points 
of  temperature.  Fortunately  Nature  furnishes  us  with  two 
convenient  standards.  It  is  found  that  under  ordinary  at- 
mospheric pressure  ice  always  melts  at  the  same  temperature, 
called  the  melting  point,  or,  more  commonly,  the  freezing  point 
(inasmuch  as  water  freezes  and  ice  melts  at  the  same  tempera- 


152 


MOLECULAR  ENERGY.  —  HEAT. 


Fig.  111. 


ture).      Again,  the  temperature  of  steam  rising  from  boiling 
water  under  the  same  pressure  is  always  the  same. 

§  120.  Graduation  of  thermometers. — The  bulb  of  a 
thermometer  is  first  placed  in  melting  ice,  and  allowed  to  stand 
until  the  surface  of  the  mercury  becomes  stationary,  and  a  mark 
is  made  upon  the  stem  at  that  point,  and  indicates  the  freezing 
point.  Then  the  instrument  is  suspended  in  steam  rising  from 
boiling  water,  so  that  all  but  the  very  top  of  the  column  is  in  the 
steam.  The  mercury  rises  in  the  stem  until  its  temperature  be- 
comes the  same  as  that  of 
the  steam,  when  it  again 
becomes  stationar}*,  and 
another  mark  is  placed 
upon  the  stem  to  indicate 
the  boiling  point.  Then 
the  space  between  the  two 
points  found  is  divided  into 
a  convenient  number  of 
equal  parts  called  degrees, 
and  the  scale  is  extended 
above  and  below  these 
points  as  far  as  desirable. 
Two  methods  of  division 
are  adopted  in  this  coun- 
try: by  one,  the  space  is 
divided  into  180  equal 
parts,  and  the  result  is 
called  the  Fahrenheit 
scale,  from  the  name  of  its  author ;  by  the  other,  the  space  is 
divided  into  100  equal  parts,  and  the  resulting  scale  is  called 
centigrade,  which  means  one  hundred  steps.  In  the  Fahrenheit 
scale,  which  is  generally  employed  for  ordinaiy  household  pur- 
poses, the  freezing  and  boiling  points  are  marked  respectively 
32°  and  212°.  The  0  of  this  scale  (32°  below  freezing  point), 


F.          ( 
Water  boils             .'212°  

A 
ter 

100°  

38. 

np. 
373°...  1 

Blood  heat  

98°..,... 

37°  

310°    . 

Max.  den.  of  water  . 

39.2°.... 
3-2°  

4°  
0°  

277°... 
273°... 

degrees. 

Mercury  freezes  

—37.8°. 

-38.8°. 

234.2°. 

1 
E 

fl 

i 

c 

No  heat  

^60°.. 

—273°.. 

0°  

CONVERSION   FROM   ONE  SCALE  TO   THE   OTHER.    153 

which  is  about  the  lowest  temperature  that  can  be  obtained  by  a 
mixture  of  snow  and  salt,  was  incorrectly  supposed  to  be  the 
lowest  temperature  attainable.  The  centigrade  scale,  which  is 
generally  employed  by  scientists,  has  its  freezing  and  boiling 
points  more  conveniently  marked,  respectively  0°  and  100°.  A 
temperature  below  0°  in  either  scale  is  indicated  by  a  minus  sign 
before  the  number.  Thus,  -12°F.  indicates  12°  below  0°  (or 
44°  below  freezing  point),  according  to  the  Fahrenheit  scale. 
Under  F.  and  C.,  Figure  111,  the  two  scales  are  placed  side  by 
side,  so  as  to  exhibit  at  intervals  a  comparative  view. 

§  121.  Conversion  from  one  scale  to  the  other.  —  Since 
100° C.  =  180° F.,  5°C.  =9°F.,  or  1°C.  =  f  of  1°F.  Hence, 
to  convert  centigrade  degrees  into  Fahrenheit  degrees,  we  mul- 
tiply the  number  by  -f ;  and  to  convert  Fahrenheit  degrees  into 
centigrade  degrees  we  multiply  by  -f .  In  finding  the  temperature 
on  one  scale  that  corresponds  to  a  given  temperature  on  the  other 
scale,  it  must  be  remembered  that  the  number  that  expresses 
the  temperature  on  a  Fahrenheit  scale  does  not,  as  it  does  on  a 
centigrade  scale,  express  the  number  of  degrees  above  freezing 
point.  For  example,  52°  on  a  Fahrenheit  scale  is  not  52°  above 
freezing  point,  but  52°  -  32°  =  20°  above  it. 

Hence,  to  reduce  a  Fahrenheit  reading  to  a  centigrade  read- 
ing, first  subtract  32  from  the  given  number,  and  then  multiply 
by%.  Thus,  f(F-32)  =  C. 

To  change  a  centigrade  reading  to  a  Fahrenheit  reading,  first 
multiply  the  given  number  by  |-,  and  then  add  32.     Thus, 
f  C  +  32  =  F. 

PROBLEMS. 

1.  The  difference  between  two  temperatures  is  80  centigrade  de- 
grees.    What  is  the  difference  in  Fahrenheit  degrees? 

2.  When  the  temperature  of  a  room  falls  30  Fahrenheit  degrees, 
how  many  centigrade  degrees  is  its  temperature  lowered? 

3.  Suppose  the  temperature  of  the  above  room  before  the  fall  was 
68° F.,  (a)  what  was  its  temperature  after  the  fall?     (ft)  What  were  the 


154 


MOLECULAR  ENERGY.  —  HEAT. 


temperatures  of  the  room  before  and  after  the  fall,  according  to  a 
centigrade  thermometer? 

4.  Express  the  following  temperatures  of  the  centigrade  scale  in  the 
Fahrenheit  scale  :  100° ;  40° ;  56° ;  60° ;  0° ;  -  20° ;  -  40° ;  80° ;  150°. 

NOTE.  —  In  adding  or  subtracting  32°,  it  should  be  done  algebraically. 
Thus,  to  change  —  14°  C.  to  its  equivalent  on  the  Fahrenheit  scale  :  §  X 
(—  14)  =  —  25.2 ;  —  25.2°  +  32°  =  6.8°,  the  required  temperature  on  the 
Fahrenheit  scale.  Again,  to  find  the  equivalent  of  24°  F.  in  the  centi- 
grade scale  :  24—  32  =  —  8;  —  8  X  f  =  —  4f ;  hence,  24°  F.  is  equiva- 
lent to  —  4.4°  +  C. 

5.  Express  the  following  temperatures  of  the  Fahrenheit  scale  in 
the  centigrade  scale  :   212° ;  32° ;  90° ;   77° ;  20° ;  10° ;  -  10° ;  -  20° ; 

-40°;  40°;  59°;  329°. 

§  122.   Air  thermometer.  —  Prepare  apparatus  as   shown  in 
Figure  112.     A  is  a  glass  flask  of  about  one-fourth  liter  capacity,  tightly 
Fig.  112.     stopped.    Through  the  stopper  extends  a  glass  tube  about  60cm 
long,  which  also  passes  through  the  stopper  of  a  bottle  B, 
partly  filled  with  colored  water.   The  latter  stopper  is  pierced 
by  a  hole  a  to  allow  air  to  pass  in  and  out  freely.     A  strip  of 
paper  C,  containing  a  scale  of  equal  parts,  is  attached  to  the 
tube  by  means  of  slits  cut  in  the  paper. 

Grasp  the  flask  with  the  palms  of  both  hands,  and  thereby 
heat  the  air  in  the  flask  and  cause  it  to  expand  and  escape 
through  the  liquid  in  bubbles.  When  several  bubbles  have 
escaped,  remove  the  hands,  and  the  air,  on  cooling,  will  con- 
tract, and  the  liquid  will  rise  and  partly  fill  the  tube. 

The  apparatus  described  is  usually  called  an  air  ther- 
mometer;  but  it  is,  more  correctly  speaking,  a  tliermo- 
scope.  It  renders  slight  changes  of  temperature  much 
more  perceptible  than  a  mercury  thermometer,  and 
therefore  is  said  to  be  more  sensitive.  For  instance,  if 
an  air  thermometer  and  a  mercury  thermometer,  whose 
bulbs  are  of  the  same  size,  are  carried  from  a  cold 
room  into  a  warm  room,  or  vice  versa,  the  changes  in 
B  the  hight  of  the  liquid  column  in  the  air  thermometer 
will  be  much  greater  and  more  rapid  than  in  the  mer- 
cury thermometer.  In  the  former,  the  temperature  is  measured 
by  the  expansion  of  air ;  in  the  latter,  by  the  expansion  of  iner- 


ABSOLUTE  TEMPERATURE.  155 

cury.  (Why  is  the  former  more  sensitive  than  the  latter?) 
This  simple  air  thermometer  cannot  have  a  fixed  scale  showing 
the  temperature  in  Fahrenheit  or  centigrade  degrees  as  a  mercury 
thermometer  does,  inasmuch  as  the  hight  of  the  liquid  column  is 
affected  by  atmospheric  pressure  as  well  as  by  temperature,  so 
that  when  the  temperature  remains  the  same,  variations  occur 
corresponding  to  the  changes  of  the  barometric  column.  But 
in  many  scientific  investigations  a  good  air  thermometer  is  better 
than  one  containing  mercury.  The  thermopile  and  galvanome- 
ter (see  page  236)  constitute  a  still  more  sensitive  apparatus 
for  showing  changes  in  temperature. 

§  123.  Measurement  of  extreme  temperatures.  —  Mer- 
cury boils  at  350°  C.  (662°  F.)  and  freezes  at  about  —39° 
C.,  and  therefore  cannot  be  used  for  indicating  tempera- 
tures above  or  below  these  points.  Extremely  high  tempera- 
tures are  measured  by  the  expansion  of  solids,  usually  a  rod  of 
platinum,  and  the  instrument  used  for  this  purpose  is  called  a 
pyrometer.  Alcohol  is  used  in  thermometers  employed  to  meas- 
ure extremely  low  temperatures.  The  air  thermometer  may  be 
used  at  any  temperature  that  will  not  soften  the  bulb  and  tube. 

§  124.  Absolute  temperature.  — If  a  body  of  air  at  0°C. 
is  heated,  its  volume  is  increased  ^^  of  the  original  volume  for 
every  degree  its  temperature  is  raised.  At  273°  C.  its  volume 
is  consequently  doubled.  If  a  body  of  air  is  cooled  below  0°  C., 
its  volume  is  diminished  for  every  degree  its  temperature  is  low- 
ered YTJ  °f  its  volume  at  0° ;  and  so,  if  its  volume  were  to  con- 
tinue to  decrease  at  that  rate  until  it  should  reach  —  273°C., 
mathematically  speaking  its  volume  would  become  nothing ;  but, 
practically,  the  air  would  cease  to  be  a  gas,  and  would  become  a 
compact,  motionless  mass  ;  that  is,  all  molecular  motion  would 
cease  at  that  point,  and  so  the  point  of  no  heat  would  be  reached. 
This  point  is  called  the  absolute  zero,  and  temperature  reckoned 
from  this  point  is  called  absolute  temperature.  On  this  scale  all 
temperatures  would  be  positive. 


156  MOLECULAR  ENERGY.  —  HEAT. 

NOTE. — Air  and  all  other  gases  we  know  (see  page  20)  are  con- 
verted into  liquids  and  solids  long  before  they  reach  the  temperature 
of  —273°  C. ;  so,  of  course,  they  cease  to  obey  the  law  of  Mariotte 
(page  59).  Though  a  body  has  never  been  cooled  to  the  absolute  zero, 
there  are  reasons,  far  more  conclusive  than  the  one  given,  which  justify 
us  in  believing  that  all  molecular  motion  would  cease  at  a  point  very 
near  — 273°  C.  In  the  further  study  of  heat,  the  use  of  the  scale  of 
absolute  temperature  is  a  great  convenience. 

The  absolute  temperature  (based  on  the  above  theory)  may 
be  found  by  adding  273  to  its  reading  on  a  centigrade  thermome- 
ter, or  459  to  its  reading  on  a  Fahrenheit  thermometer.  (See 
Figure  111.) 

§  125.  Laws  of  gaseous  bodies.  —  It  follows,  from  the 
above  discussion,  that  the  volume  of  a  given  mass  of  gas  at  con- 
stant pressure  is  proportional  to  its  absolute  temperature.  This 
is  called  the  Law  of  Charles. 

If,  however,  a  body  of  gas  at  0°  C.  is  enclosed  in  a  vessel  of 
rigid  sides,  its  volume  must  remain  constant  at  all  tempera- 
tures. In  this  case  the  pressure  on  the  sides  is  increased  by 
^j  of  the  pressure  at  0°  for  every  degree  its  temperature  rises, 
and  is  diminished  ^y^  for  every  degree  its  temperature  falls ;  and 
if  it  were  to  continue  to  decrease  at  this  rate,  at  —  273°  C.,  it 
would  become  nothing.  Hence,  the  pressure  of  a  given  body 
of  gas,  ivhose  volume  is  kept  constant,  is  proportional  to  its  abso- 
lute temperature. 

Mariotte's  law  states  that  at  a  constant  temperature  the  vol- 
ume of  a  given  body  of  gas  is  inversely  proportional  to  the 
pressure  to  which  it  is  subjected;  i.e.,  the  product  of  the  pressure 
and  the  volume  is  constant.  Now,  when  both  the  pressure  and 
the  volume  vary  at  the  same  time,  it  is  evident  that  the  prod- 
uct of  the  pressure  and  the  volume  of  a  given  body  of  gas  is 
proportional  to  its  absolute  temperature. 

PROBLEMS. 

1.  Find  in  both  centigrade  and  Fahrenheit  degrees  the  absolute  tem- 
peratures at  which  mercury  boils  and  freezes. 

2.  At  0°  C.  the  volume  of  a  certain  body  of  gas  is  500ccm  under  a 
constant  pressu're ;  (a)  what  will  be  its  volume  if  its  temperature  is  raised 


KINETIC   THEORY   OF    GASES.  157 

to75°C.?    (&)  What  will  be  its  volume  if  its  temperature  becomes 
-20°  C.? 

3.  If  the  volume  of  a  body  of  gas  at  20°  C.  is  200ccm,  what  will  be  its 
volume  at  30°  C.?    Solution :  20°  C.  is  equivalent  to  (20  +  273)  293  abs. 
temp. ;  then  293  :  303  : :  200  :  206.8ccm.     Ans. 

4.  To  what  volume  will  a  liter  of  gas  contract  if  cooled  from  30°  C. 
to  -15°C.? 

5.  One  liter  of  gas  under  a  pressure  of  one  atmosphere  will  have 
what  volume  if,  at  a  constant  temperature,  the  pressure  is  reduced  to 
9008  per  square  centimeter? 

6.  The  volume  of  a  certain  body  of  air  at  a  temperature  of  17°  C. , 
and  under  a  pressure  of  800s  per  square  centimeter,  is  500ccm ;  what  will 
be  its  volume  at  a  temperature  of  27°  C.  under  a  pressure  of  12008  per 
square  centimeter?     Solution:  17°  C.  is  equivalent  to  290°  abs.  temp.; 
27°  C.  is  equivalent  to  300°  abs.  temp.     Then  290 : 300  : :  500  X  800  :  x  X 
1200.     Whence  x=  344. 8CC.     Ans. 

7.  If  the  volume  of  a  body  of  gas  under  a  pressure  of  lk  per  square 
centimeter,  and  at  a  temperature  of  0°  C.,  is  1  liter,  at  what  temperature 
will  its  volume  be  reduced  to  lccm  under  a  pressure  of  200k  per  square 
centimeter?    Ans. :  54.6°  abs.  temp.,  or  —  218.4°  C. 

8.  Find  the  temperatures  on  the  absolute  scale  at  which  bodies 
named  on  page  161  melt  or  boil. 

9.  If  a  cubic  foot  of  coal-gas  at  32°  F.,  when  the  barometer  is  at 
30  in.,  weighs  ^  lb.,  how  much  will  an  equal  volume  weigh  at  68°  F. 
when  the  barometer  is  at  29  in.? 

§  126.  Kinetic  theory  of  gases.  —  This  theory  claims  that 
in  gases  the  molecules  are  so  far  separated  from  each  other  that 
their  motions  are  not  generally  influenced  by  molecular  attrac- 
tions. Hence,  in  accordance  with  the  first  law  of  motion,  the 
molecules  of  gases  move  in  straight  lines  and  with  uniform  ve- 
locit}',  until  they  collide  with  each  other  or  strike  against  the 
walls  of  the  containing  vessel,  when,  in  consequence  of  their 
elasticity,  they  at  once  rebound  and  start  on  a  new  path.  We 
may  picture  to  ourselves  what  is  going  on  in  a  body  of  calm 
air,  for  instance,  by  observing  a  swarm  of  bees,  when  every 
individual  bee  is  flying  with  great  velocity,  first  in  one  direction 
and  then  in  another,  while  the  swarm  either  remains  at  rest  or 
sails  slowly  through  the  air. 


158  MOLECULAR   ENERGY.  —  HEAT. 

§  127.  Pressure  of  a  gas  due  to  the  kinetic  energy  of  its 
molecules.  —  Consider,  then,  what  a  molecular  storm  must  be 
raging  about  us,  and  how  it  must  beat  against  us  and  against 
every  exposed  surface.  According  to  the  kinetic  theory,  the 
pressure  of  a  gas  (or  its  expansive  power  as  it  is  sometimes 
called) ,  is  entirely  due  to  the  striking  of  the  molecules  against  the 
surfaces  on  which  the  gas  is  said  to  press,  the  impulses  following 
each  other  in  such  rapid  succession  that  the  effect  produced  can- 
not be  distinguished  from  constant  pressure.  Upon  the  kinetic 
energy  of  these  blows,  and  upon  the  number  of  blows  per 
second,  must  depend  the  amount  of  pressure.  But  we  saw  on 
page  141,  that  on  the  energy  of  the  individual  molecules  depends 
that  condition  of  a  gas  called  its  temperature;  so,  it  is  apparent, 
as  stated  above,  that  the  pressure  of  a  given  quantity  of  gas  varies 
as  its  temperature.  Again,  as  at  the  same  temperature  the  num- 
ber of  blows  per  second  must  depend  upon  the  number  of  mole- 
cules in  the  unit  of  space,  it  is  apparent  that  the  pressure  varies 
as  the  density. 

The  following  estimates1  made  for  hydrogen  molecules  at  0°C.,  and 
under  a  pressure  of  one  atmosphere,  may  prove  interesting :  — 

Mean  velocity,  6100  feet  per  second. 

Mean  path  without  collision,  38  ten-millionths  of  an  inch. 

Collisions,  17,750  millions  per  second. 

Mass,  216,000  million  million  million  weigh  1  gram. 

Number,  19  million  million  million  fill  1  cubic  centimeter. 

§  128.  Diffusion  of  gases  and  liquids.  —  The  kinetic  the- 
ory of  gases  explains  why  gases  penetrate  into  any  spaces  open 
to  them,  and  likewise  the  phenomenon  known  as  the  diffusion 
of  gases  (see  page  41).  The  presence  of  a  gas  in  a  given 
space  only  delays  the  spread  of  another  gas  in  the  same  space 
by  collision  between  the  molecules  of  the  inter-diffusing  gases. 
The  diffusion  between  liquids,  though  not  so  well  understood, 
is  undoubtedly  due  in  part  to  similar  molecular  motions. 

i  Maxwell. 


LIQUEFACTION  AND  VAPORIZATION.  159 


XXII.     EFFECTS   OF  HEAT   CONTINUED.  —  LIQUEFACTION 
AND   VAPORIZATION. 

Experiment  1.  Melt  separately  tallow,  lard,  and  beeswax.  When 
partially  melted,  stir  well  with  a  thermometer,  and  ascertain  the  melting 
points  of  each  of  these  substances. 

Experiment  2.    Place  a  test  tube  (Fig.  113),  half  filled  with  ether, 
in  a  beaker  containing  water  at  a  temperature  of  60°  C.     Although  the 
temperature  of  the  water  is  40°  below  its  boiling  point, 
it  very  quickly  raises  the  temperature  of  the  ether  suffi-    _    Fi°- 113- 
ciently  to  cause  it  to  boil  violently.    Introduce  a  chemi- 
cal thermometer1  into  the  test  tube,  and  ascertain  the 
boiling  point  of  ether. 

Experiment  3.  Half  fill  a  glass  beaker  of  a  liter 
capacity  with  fragments  of  ice  or  snow,  and  set  the 
beaker  into  a  basin  of  boiling-hot  water.  Stir  the  con- 
tents of  the  beaker  with  a  thermometer  until  the  ice  is 
all  melted,  observing  from  time  to  time  the  temperature  of  the  contents. 
The  temperature  remains  constant  at  0°  C.  until  the  ice  is  all  melted. 

Experiment  4.  As  soon  as  the  last  piece  of  ice  disappears,  remove 
the  flask  from  the  warm  water,  wipe  the  outside,  and  place  it  over  a 
Bunsen  burner  and  heat.  Observe  that  the  temperature  rises  con- 
stantly until  the  water  begins  to  boil ;  but  after  it  begins  to  boil,  the 
temperature  remains  constant  as  long  as  it  boils.  Place  more  burners 
under  the  beaker ;  the  water  boils  more  violently,  but  the  temperature 
is  not  raised. 

Experiment  5.  Place  in  contact  the  smooth,  dry  surfaces  of  two 
pieces  of  ice;  press  them  together  for  a  few  seconds;  remove  the 
pressure,  and  they  will  be  found  firmly  frozen  together.  The  ice  at  the 
surfaces  of  contact  melts  under  the  pressure,  but  when  the  pressure  is 
removed  the  liquid  instantly  freezes  and  cements  the  pieces  together. 
It  is  in  this  manner  that  snow-balls  are  formed. 

NOTE.  —  If  a  thermometer  is  placed  in  a  mixture  of  ice  and  water, 
and  the  mixture  is  subjected  to  great  pressure,  some  of  the  ice  will 
melt  and  the  temperature  will  fall;  but  when  the  pressure  is  removed, 
a  portion  of  the  water  freezes  and  the  temperature  rises.  From  this 
we  learn  that  the  melting  (or  freezing}  point  of  water  is  very  slightly  low- 
ered by  pressure.  The  depression  is  about  Tf,r  of  1°  C  for  each  atmos- 
phere. On  the  other  hand,  it  is  found  that  substances  which,  unlike  ice, 
expand  in  melting,  have  their  melting  points  raised  by  pressure. 

1 A  chemical  thermometer  has  its  scale  on  the  glass  stem,  instead  of  a  metal  plate, 
and  is  otherwise  adapted  to  experimental  use. 


160 


MOLECULAR  ENERGY.  —  HEAT. 


Experiment  6.  Half  fill  a  thin  glass  flask  witn  water.  Boil  the 
water  over  a  Bunsen  burner;  the  steam  will  drive  the  air  from  the 

flask.  Withdraw  the  burner,  quickly 
cork  the  flask  very  tightly,  and  plunge 
the  flask  into  cold  water,  or  invert  the 
flask  and  pour  cold  water  upon  the  part 
containing  steam,  as  in  Figure  114 ;  the 
water  in  the  flask,  though  cooled  several 
degrees  below  the  usual  boiling  point, 
boils  again  violently.  The  application 
of  cold  water  to  the  flask  condenses 
some  of  the  steam,  and  diminishes  the 
tension  of  the  rest,  so  that  the  pressure 
upon  the  water  is  diminished,  and  the 
water  boils  at  a  reduced  temperature. 

If  hot  water  is  'poured  upon 
the  flask,  the  water  ceases  to  boil. 
(Why  ?)  Under  the  receiver  of  an 
air-pump,  water  may  be  made  to 
boil  at  any  temperature  between 

0°  and  100°  C. ;  indeed,  if  exhaustion  is  carried  far  enough, 
boiling  and  freezing  may  be  going  on  at  the  same  time.  When 
high  temperature  is  objectionable,  apparatus  is  contrived  for 
boiling  and  evaporating  in  a  vacuum  ;  as,  for  instance,  in  the 
vacuum  pans  used  in  sugar  refineries.  As  water  boils  more 
easily  under  diminished  pressure,  so  it  boils  with  more  difficulty 
when  the  pressure  is  increased ;  and  the  temperature  to  which 
water  may  be  raised  under  the  pressure  of  its  own  steam  is 
only  limited  by  the  strength  of  the  vessel  containing  it.  Ves- 
sels of  this  kind  are  often  employed  to  effect  a  complete  pene- 
tration of  water  into  solid  and  hard  substances.  By  this  means 
gelatine  is  extracted  from  the  interior  of  bones.  In  the  boiler 
of  a  locomotive,  where  the  pressure  is  sometimes  150  Ibs.  above 
the  atmosphere,  the  boiling  point  rises  to  about  180°  C.  (360°  F.). 

Experiment  7.  Dissolve  table-salt  in  water,  and  you  may  raise 
its  boiling  point  till  it  reaches  108°  C.  With  saltpetre  it  may  reach 
115°  C. 


LAWS  OF   FUSION   AND   BOILING. 


161 


On  the  other  hand,  it  is  well  known  that  sea-water,  which  con- 
tains saline  matter  in  solution,  freezes  at  a  lower  temperature 
than  0°  C.  From  the  above  experiments,  and  others  of  a  similar 
nature,  we  derive  the  following 


LAWS  OF  FUSION  AND  BOILING. 


1.  The    temperature    at    which 
solids  melt  differs  for  different  sub- 
stances,  but  is  invariable  for  the 
same  substance,  if  the  pressure  is 
constant.     Substances  solidify  usu- 
ally at   the  same  temperatures  as 
those  at  which  they  melt. 

2.  After  a  solid  begins  to  melt, 
the   temperature    remains    constant 
until  the  whole  is  melted. 

3.  Pressure  lowers  the  melting  (or 
solidifying}  point  of  substances  that 
expand  on  solidifying,  and  raises  the 
melting  point  of  those  that  contract. 

4.  The  freezing  point  of  water  is 
lowered  by  the  presence  of  salts  in 
solution. 


1.  The    temperature    at    which 
liquids  boil  differs  for  different  sub- 
stances,  but  is  invariable  for    the 
same  substance  if  the  pressure  is 
constant.       Vapors    liquefy  at   the 
same  temperatures  as  those  at  which 
they  boil. 

2.  After  a  liquid  begins  to  boil 
the  temperature   remains    constant 
until  the  whole  is  vaporized. 

3.  Pressure    raises   the  boiling 
point  of  all  substances. 


4.  The  boiling  point  of  water  is 
raised  by  the  presence  of  salts  in 
solution. 


REFERENCE  TABLES. 
Melting  Points. 


Alcohol Never  frozen. 

Mercury -  38.8°  C. 

Sulphuric  acid -34.4° 

Ice 0° 

Phosphorus 44° 

Sulphur 115° 

Tin about  233° 

Lead..  "       334° 


Zinc about 425°  C. 

Silver "     1000° 

Gold t "     ....1200° 

Cast-iron "  1050-1250° 

Wrought-iron  ....  "  1500-1600° 
Iridium  (the  most 

infusible  metal) 

about..  ..1950° 


Boiling  Points  under  a  Pressure  of  one  Atmosphere. 

Carbonic  acid -  78°  C. 

Ammonia —  40° 

Sulphurous  acid —  10° 

Ether  ..  35° 


Carbon  bisulphide 48°  C. 

Alcohol 78° 

Water 100° 

Mercury 35.,° 


162 


MOLECULAR  ENERGY.  —  HEAT. 


Boiling  Points  of  Water  at  Different  Pressures. 

Atmospheres. 

212°  F 1 

249.5° 2 

273.3° 3 

306°     5 

356.6°..  ..10 


Barometer. 

184°  F 16.68  inches. 

190°      18.99      " 

200°      23.45      " 

210°      28.74      " 

212°  ..29.92      " 


The  temperature  of  the  boiliug  point  of  water  varies  with  the  alti- 
tude of  places,  in  consequence  of  the  different  atmospheric  pressure. 
A  difference  of  altitude  of  533  ft.  causes  a  variation  of  1°F.  in  the 
boiling  point. 

Boiling  Points  of  Water  at  Different  Altitudes. 

Above  the 
sea-level. 

Quito +  9,500  ft. . 

Mont  Blanc 15,650  "  . 

Mt.  Washington *  6,290  "  . 

Boston 0  "  . 

Dead  Sea  (below) -  1,316  "  . 

§129.    Distillation. — Apparatus  like   that  represented  in 

Figure  115  may  be 

Fig.  115. 

easily  constructed. 
The  following  ex- 
periment will  be 
found  interesting 
and  instructive. 


Mean  hight  of 
Barometer.       Temperature. 

..21.53  in  195.8°  F. 

..16.90  " 

186° 

..22.90  " 

200° 

.  .30.       " 

212° 

..31.50  " 

214° 

Experiment.  Half 
fill  the  flask  A  with 
water  colored  with  a 
few  drops  of  ink. 
Boil  the  water,  and 
the  steam  arising  will 
escape  through  the 
glass  delivery  tube 

BB.  This  tube  is  surrounded  in  part  by  a  larger  tube  C,  called  a  con- 
denser, which  is  kept  filled  with  cold  water  flowing  from  a  vessel  D 
through  a  siphon  S,  the  water  finally  escaping  through  the  tube  E. 


EVAPORATION.  168 

The  steam  is  condensed  in  its  passage  through  the  delivery  tube,  and 
the  resulting  liquid  is  caught  iii  the  vessel  F.  The  liquid  caught  is 
colorless.  A  complete  separation  of  the  watery  portion  of  the  colored 
liquid  from  the  other  ingredients  of  the  ink  is  effected,  the  latter  being 
left  in  the  flask  A. 

The  separation  is  accomplished  on  the  principle  that  the  tem- 
perature of  the  boiling  points  of  different  substances  differ.  The 
water  is  raised  to  its  vaporizing  point,  but  the  other  substances 
are  not.  The  apparatus  is  called  a  still,  and  the  operation 
distillation. 

If  a  volatile  liquid,  such  as  alcohol,  is  to  be  separated  from 
water,  the  mixture  is  heated  to  the  temperature  at  which  the 
volatile  liquid  boils,  but  not  to  the  boiling  point  of  water,  when 
the  alcohol  will  pass  into  the  vessel  JT,  and  the  water,  for  the 
most  part,  will  remain  in  the  flask. 

§  130.  Evaporation.  —  In  boiling,  the  heat,  usually  ap- 
plied at  the  bottom,  rapidly  converts  the  liquid  into  vapor, 
which,  rising  in  bubbles  and  breaking  at  or  near  the  surface, 
produces  a  violent  agitation  in  the  liquid,  sometimes  called 
ebullition. '  Evaporation  is  that  form  of  vaporization  which  takes 
place  quietly  and  slowly  at  the  surface.  The  phenomena  and 
laws  of  vaporization  of  all  liquids  are  similar,  but  we  will  study 
only  the  important  case  of  water.  Although  hastened  by  heat, 
the  evaporation  of  water  occurs  at  any  temperature,  however 
low  ;  even  ice  and  snow  evaporate. 

The  rapidity  of  evaporation  varies  directly  ivith  the  tempera- 
ture, amount  of  surface  exposed,  and  dryness  of  the  atmosphere, 
and  inversely  with  the  pressure  upon  the  liquid.  This  vapor  of 
water  mixes  freely  with  the  air,  and  diffuses  readily  through  it, 
acting  like  another  gas  (compare  pages  42  and  158).  The  air 
does  not  take  up  water  like  a  sponge,  as  is  commonly  imagined  ; 
for,  if  the  air  could  be  removed  from  a  room,  where  there  is  a 
large  vessel  of  water,  every  cubic  foot  of  the  space  in  the  room 
would  be  found  to  contain  just  as  much  water-vapor  as  it  does 


164  MOLECULAR    ENERGY.  —  HEAT. 

when  the  air  is  present,  —  probably  a  very  little  more.  In  either 
case,  only  a  definite  quantity  would  be  found  in  each  cubic  foot, 
a  quantity  depending  on  the  temperature  of  the  space.  Thus,  at 
0°C.,  each  cubic  foot  can  contain  0.14*;  at  10°,  0.26g  ;  at  20°, 
0.49g;  and  at  30°,  0.85g.  Evidently  the  capacity  is  nearly 
doubled  by  a  rise  of  10°  in  temperature. 

§  131.  Dew  point.  —  When  a  space  contains  such  an 
amount  of  water-vapor,  whether  it  contains  other  gases  or  not, 
that  its  temperature  cannot  be  lowered  without  some  of  the  water 
being  precipitated  in  the  form  of  a  liquid,  the  space  is  said  to  be 
saturated,  and  the  temperature  is  called  the  deiv  point.  The  form 
in  which  the  condensed  vapor  appears  is,  according  to  its  loca- 
tion, dew,  fog,  or  cloud.  The  atmosphere  is  said  to  be  dry  or 
humid,  according  as  the  difference  between  the  dew  point  and 
the  temperature  of  the  atmosphere  is  great  or  little. 

QUESTIONS. 

1.  Why  does  our  breath  produce  a  cloud  in  winter  and  not  in  sum- 
mer? 

2.  (a)  If  air  at  0°  is  warmed  to  20°  C.,  how  will  its  dryness  be 
affected?    (&)  What  effect  would  such  warmed  air  have  on  wet  clothes? 

3.  If  saturated  air  at  20°  is  blown  into  a  cellar  where  the  tempera- 
ture is  10°,  what  will  happen? 

4.  What  is  the  cause  of  the  general  complaint  of  dryuess  of  air  in 
rooms  heated  by  stoves  or  furnaces? 

5.  Does  a  given  mass  of  air  in  such  a  room  contain  less  water-vapor 
than  an  equal  mass  of  cold  out-door  air  at  the  same  time? 


HEAT    UNITS.  165 


XXIII.     HEAT  CONVERTIBLE  INTO  POTENTIAL  ENERGY,  AND 
VICE  VERSA. 

§  132.  Heat  units.  —  It  is  frequently  necessary  to  measure 
quantity  of  heat,  and  for  this  purpose  a  standard  unit  of  measure- 
ment is  required.  The  heat  unit  generally  adopted  is  the  amount 
of  heat  required  to  raise  the  temperature  of  one  kilogram  of  water 
from  OP  to  1°  C.  This  unit  is  called  a  calorie. 

Let  it  be  required  to  find  the  amount  of  heat  that  disappears 
(Exp.  3,  p.  159)  during  the  melting  of  one  kilogram  of  ice. 

Experiment  1.  Place  lk  of  ice  at  0°  C.  in  a  beaker,  and  the  beaker 
in  a  large  basin  of  boiling  water  (Fig.  116),  and  at  the  same  instant 
place  in  the  hot  water  another  beaker  containing  lk  of  water  at  0°  C. 
Place  in  each  beaker  a  thermometer,  and  at  the  instaut  that  the  ice 
disappears  note  the  temperature 
of  the  water  in  each;  it  will  be 
found  that  while  the  temperature 
of  the  former  has  not  changed, 
the  latter  has  risen  to  about  80°  C. 

It  is  evident  that  the  contents 
of  both  beakers  must  have  re- 
ceived the  same  amount  of  heat ; 
hence,  the  amount  of  heat  re- 
ceived by  the  water  being  80 
calories,  the  amount  of  heat  that  cksappe&rs  or  is  lost  during  the 
melting  of  one  kilogram  of  ice  is  80  calories. 

Next,  let  it  be  required  to  find  the  amount  of  heat  that  dis- 
appears (Exp.  4,  p.  159)  during  the  conversion  of  lk  of  water 
into  steam. 

Experiment  2.  Place  lk  of  water  at  0°  C.  in  a  beaker,  and  heat  the 
same  with  a  Bunsen  burner.  Note  the  time  that  it  takes  to  raise  the 
water  from  0°  C.  to  100°  C.,  also  the  time  during  which  the  temperature 
of  the  water  remains  stationary  while  the  water  is  boiling  away.  The 
latter  time  will  be  found  to  be  about  five  times  the  formert 

Now,  as  the  water  receives  100  calories  during  the  time  it  is 


166  MOLECULAR    ENERGY.  —  HEAT. 

rising  from  the  freezing  to  the  boiling  point,  it  must  receive  about 
500  calories  during  the  time  it  is  converted  into  steam  :  but  the 
temperature  of  the  water  is  not  changed  during  the  latter  oper- 
ation. More  accurate  methods  have  the  number  537  ;  so  it  fol- 
lows that  537  calories  disappear,  or  are  lost  during  the  conversion 
of  1  kilogram  of  water  into  steam. 

§  133.  Two  questions  answered.  —  Inasmuch  as  none  of 
the  heat  applied  during  the  melting  of  ice  and  the  conversion 
of  water  into  steam  raises  the  temperature  of  the  body  to 
which  it  is  applied,  the  question  arises,  What  does  the  heat  do? 
Again,  Why  is  not  ice  instantly  converted  into  water  on  reach- 
ing the  melting  point,  and  water  instantly  converted  into  steam  on 
reaching  the  boiling  point  f 

The  answer  to  the  first  question  is,  All  of  the  heat  applied  in 
melting  ice  is  consumed  in  doing  interior  work,  as  it  is  called. 
The  molecules  that  were  firmly  held  in  their  places  by  molecular 
forces  are  now  moved  from  their  places,  and  so  work  is  done 
against  these  forces,  just  as  work  is  done  against  gravity  when 
a  weight  is  lifted.  In  the  conversion  of  water  into  steam,  a 
similar  action  goes  on ;  the  heat  is  expended  in  separating 
the  molecules  so  far  that  the  molecular  attractive  forces  are  no 
longer  sensible,  all  except  the  small  fraction  used  in  overcoming 
atmospheric  pressure.1  Heat,  the  energy  of  motion,  in  both 
instances  does  important  work,  and  is  thereby  converted  into 
the  energy  of  position,  or  potential  energy,  —  energy  of  the 
same  kind  as  that  of  a  raised  weight. 

The  answer  to  the  second  question  is,  The  amount  of  work- 
done  in  both  instances  is  great,  as  shown  by  the  amount  of  heat 
consumed  in  doing  the  work ;  80  calories  per  kilogram  of  ice 
being  required  in  the  first  instance,  and  537  calories  per  kilo- 
gram of  water  in  the  second ;  hence  it  requires  a  long  time  to 
acquire  the  requisite  amount  of  heat.  It  is  fortunate  that  it 
takes  a  large  quantity  of  heat  to  melt  ice  ;  otherwise,  on  a  single 


COLD   BY   SOLUTION.  167 

warm  day  in  winter,  all  the  ice  and  snow  would  melt,  creating 
most  destructive  freshets.  The  heat  which  disappears  in  melting 
and  boiling  is  generally,  but  with  our  present  knowledge  of  the 
subject,  rather  objectionably,  called  latent  (hidden)  heat.  The 
error  consists  in  calling  that  heat  which  has  ceased  to  be  heat, 
i.e.,  has  ceased  to  be  molecular  motion. 

§  134.  Methods  of  producing-  artificial  cold. — The  fact 
that  heat  must  be  consumed  because  work  is  done,  in  the  con- 
version of  solids  into  liquids  and  liquids  into  vapors,  and  in  the 
simple  expansion  of  gases,  is  turned  to  practical  use  in  many 
ways  for  the  purpose  of  producing  artificial  cold.  They  are 
embraced  under  three  heads;  viz.,  Cold  produced  by  solution, 
by  evaporation,  and  by  expansion  of  gases.  The  following  ex- 
periments will  illustrate. 

§  135.  Cold  by  solution.  — Freezing  mixtures.  — Experi- 
ment. Prepare  a  mixture  of  2  parts  by  weight  of  pulverized  ammo- 
nium nitrate  and  1  part  of  ammonium  chloride,  and  dissolve  in  3 
parts  of  water  (not  warmer  than  10°  C.),  stirring  the  same  while 
dissolving  with  a  test-tube  containing  a  little  water.  The  water  in  the 
test  tube  will  be  quickly  frozen.  A  finger  Fig. 

placed  in  the  solution  will  feel  a  painful 
sensation  of  cold,  and  a  thermometer  will 
indicate  a  temperature  of  about  — 10°  C. 

One  of  the  most  common  freezing 
mixtures  consists  of  3  parts  of  snow  or 
broken  ice  and  1  part  of  common  salt. 
The  affinity  of  salt  for  water  causes  a 
liquefaction  of  the  ice,  and  the  result- 
ing liquid  dissolves-the  salt,  both  oper- 
ations requiring  heat. 

§  136.  Cold  by  evaporation.  —  Experiment  1.  Fill  the  palm 
of  the  hand  with  ether ;  the  ether  quickly  evaporates  and  produces  a 
painful  sensation  of  cold. 

Experiment  2.  Place  water  at  about  10°  C.  in  a  thin  porous  cup, 
such  as  is  used  in  the  Grove's  battery  (see  page  190),  and  introduce 


168         MOLECULAR  ENERGY.  —  HEAT. 

the  bulb  of  a  thermometer ;  although  the  experiment  be  conducted  in  a 
warm  room,  the  large  surface  exposed  by  meaus  of  the  porous  vessel 
will  so  hasten  evaporation  that  in  the  course  of  fifteen  minutes  there 
will  be  a  very  sensible  fall  in  temperature. 

Experiment  3.  Cover  closely  the  bulb  of  an  air  thermometer  (Fig. 
117)  Avith  thin  muslin,  and  partly  fill  the  stem  with  water.  Let  one 
person  slowly  drop  ether  on  the  bulb  while  another  briskly  blows  the 
air  charged  with  vapor  away  from  the  bulb  with  a  bellows.  (Why  ?) 
The  water  in  the  stem  will  quickly  freeze  even  in  a  warm  room. 

QUESTIONS. 

1.  Why  do  we  bathe  the  fevered  forehead  with  alcohol  and  water  ? 

2.  How  does  perspiration  contribute  to  our  comfort  ? 

3.  Why  do  we  fan  ourselves  ? 

4.  Why  does  a  windy  day  seem  colder  to  us  than  a  still  day,  although 
the  temperature  is  the  same  on  both  days  ? 

5.  Why  do  we  blow  our  hot  tea,  and  why  pour  it  into  a  saucer? 

6.  How  does  sprinkling  a  floor  cool  the  air  of  a  room  ? 

§  137.  Cold  by  expansion  of  gases.  —  When  a  beer  bottle 
is  opened,  a  fog  is  suddenly  produced  in  the  neck  of  the  bottle 
due  to  the  chill  of  an  expanding  gas. 

The  work  done  in  the  expansion  of  a  gas  consists  only  in 
forcing  back  the  surrounding  air.  If  confined  air  is  allowed  to 
expand  into  a  vacuum,  no  work  is  done,  and  the  temperature  is 
not  changed.  By  allowing  condensed  air  containing,  as  it 
usually  does,  watery  vapor,  to  escape  suddenly  from  the  vessel 
in  which  it  is  confined,  icicles  have  been  formed  around  the 
orifice  whence  it  escapes. 

§  138.  Potential  energy  converted  into  heat  by  the 
solidification  of  liquids  and  the  liquefaction  of  vapors.— 
Experiment  1.  Boil  about  \  liter  of  water  in  a  glass  flask,  and  add, 
slowly,  pulverized  sodium  sulphate  until  the  boiling  water  refuses  to 
dissolve  more  (hot  water  will  dissolve  about  twice  its  weight  of  this 
substance).  Then  set  the  hot  solution  in  a  place  where  it  will  not  be 
disturbed,  and  let  it  stand  for  about  24  hours,  that  it  may  acquire  the 
temperature  of  the  room.  Thrust  the  bulb  of  a  thermometer  into  the 
solution,1  and  at  the  same  time  drop  in  a  lump  of  sodium  sulphate; 

1  The  solution  is  now  said  to  be  supersaturated. 


POTENTIAL   ENERGY,    ETC.  169 

solidification  instantly  sets  in,  and  in  a  few  seconds  the  liquid  mass 
will  be  almost  wholly  replaced  by  crystals.  At  the  same  time  the 
temperature,  as  indicated  by  the  thermometer,  rapidly  rises. 

The  heat  which  is  consumed  in  dissolving  a  solid,  and  in  giv- 
ing the  molecules  an  advantage  of  position,  is  restored  when  tlr: 
molecules  are  allowed  to  resume  their  original  positions,  as  n 
falling  weight  restores  the  kinetic  energy  consumed  in  raising  it. 

Experiment  2.  Place  water  at  about  10°  C.  in  a  bottle,  and  intro- 
duce a  thermometer.  Surround  the  bottle  with  a  snow  and  salt  freez- 
ing mixture ;  the  temperature  of  the  water  rapidly  falls  until  it  reaches 
0°C. 

The  heat  which  the  water  loses  is  consumed  in  melting  the  ice 
and  dissolving  the  salt.  AtO°C.  the  water  begins  to  freeze, 
and  the  temperature  remains  stationary  until  all  the  water  is 
frozen,  when  its  temperature  again  falls.  The  temperature  of 
the  freezing  mixture  is  much  lower  than  that  of  the  water  while 
freezing  ;  the  latter,  then,  must  give  heat  to  the  former.  That 
the  mixture  receives  heat  Fig  118> 

is  shown  by  the  continua- 
tion of  the  melting  and 
dissolving.  But  as  the 
temperature  of  the  water 
while  freezing  does  not 
fall,  it  must  be  that  the 
heat  which  it  surrenders 
during  solidification  arises 
from  the  conversion  into 
heat  of  the  potential  en- 
ergy possessed  by  the  molecules  of  the  liquid. 

Experiment  3.  Arrange  apparatus  as  in  Figure  118.  When  water 
iu  the  flask  A  begins  to  boil,  introduce  the  end  of  the  delivery  tube  B 
into  a  vessel  C  of  water  at  0°  C.  The  steam  that  passes  through  the 
tube  is  condensed  on  entering  the  cold  water  and  heats  the  water. 
When  a  considerable  portion  of  the  water  has  boiled  away,  weigh  the 
water  remaining  in  A,  and  ascertain  the  quantity  that  has  been  con- 


170  MOLECULAR    ENERGY.  —  HEAT. 

verted  into  steam ;  also  ascertain  the  temperature  of  the  water  in  C, 
and  the  number  of  calories  which  it  has  received. 

For  every  kilogram  of  water  that  is  converted  into  steam, 
5.37k  of  water  (practically,  considerably  less  than  this  quantity, 
in  consequence  of  loss  of  heat  by  radiation  and  evaporation 
from  C)  will  be  raised  from  0°  to  100°.  As  lk  requires  100 
units  of  heat  to  raise  it  to  100°,  the  5.37k  must  require  537  units 
of  heat.  But  the  steam  raises  the  water  to  its  own  temperature 
without  having  its  own  temperature  lowered.  (Whence  come 
the  537  units  of  heat  that  raise  the  temperature  of  the  water?) 

Heat  that  is  consumed  in  liquefying  solids,  and  in  vaporizing 
liquids,  is  always  restored  when  the  reverse  change  takes  place. 
Farmers  well  understand  that  water,  in  freezing,  gives  out  a 
great  deal  of  heat,  —  at  a  low  temperature,  it  is  time,  but  still 
high  enough  to  protect  vegetables  which  freeze  only  when  con- 
siderably colder  than  melting  ice.  The  fact  that  steam,  in 
condensing,  generates  a  large  amount  of  heat,  is  turned  to 
practical  use  in  heating  buildings  by  steam. 


XXIV.     SPECIFIC   HEAT. 

§  139.  Temperatures  of  different  substances  raised 
unequally  by  equal  quantities  of  heat.  —  Will  equal  quanti- 
ties of  heat  applied  to  equal  weights  of  different  substances 
raise  their  temperatures  equally  ? 

Experiment  1.  Mix  lk  of  water  at  0°  with  lk  at  20° ;  the  tempera- 
ture of  the  mixture  becomes  10°.  The  heat  that  leaves  lk  of  water 
when  it  falls  from  20°  to  10°  is  just  capable  of  raising  lk  of  water  from 
0°  to  10°. 

Experiment  2.  Take  (say)  300s  of  sheet  lead,  and  make  a  loose 
roll  of  it,  and  suspend  it  by  a  thread  in  boiling  water  for  about  five 
minutes,  that  it  may  acquire  the  same  temperature  (100°  C.)  as  the 
water.  Remove  the  roll  from  the  hot  water,  and  immerse  it  as  quickly 
as  possible  in  300s  of  water  at  0°,  and  introduce  the  bulb  of  a  ther- 
mometer. Note  the  temperature  of  the  water  when  it  ceases  to  rise, 
which  will  be  found  to  be  about  3°  (accurately  3.3°+).  The  lead  cools 


SPECIFIC   HEAT  DEFINED.  171 

vrery  much  more  than  the  water  warms.     Lead  falls  about  33°  for  every 
degree  an  equal  weight  of  water  is  warmed. 

From  the  first  experiment  we  infer  that  a  body,  in  cooling  a 
certain  number  of  degrees,  gives  to  surrounding  bodies  as  much 
heat  as  it  takes  to  raise  its  temperature  the  same  number  of 
degrees.  From  the  second  experiment  we  learn  that  the  quan- 
tity of  heat  that  raises  lk  of  lead  from  3.3°+  to  100°,  when 
transferred  to  water,  can  raise  lk  of  water  only  from  0°  to  3.3°. 
Hence  we  conclude  that  equal  quantities  of  heat,  applied  to  equal 
weights  of  different  substances,  raise  tlieir  temperatures  unequally. 

§  140.  Capacity  for  heat.  —  If  equal  weights  of  mercury, 
alcohol,  and  water  are  exposed  to  the  same  heat,  the  mercury 
will  rise  30°,  and  the  alcohol  nearly  2°,  while  the  water  is  rising 
1°.  From  this  we  infer  that  to  raise  a  kilogram  of  each  of 
these  substances  from  0°  to  1°  requires  30  times  as  much  heat 
for  the  water  as  for  the  mercury,  and  twice  as  much  as  for  the 
alcohol.  Since  heat  affects  the  temperature  of  water  less  than 
mercury  and  alcohol,  the  first  is  said  to  have  a  greater  capacity 
for  heat.  The  number  of  units  of  heat  required  to  raise  the  tem- 
perature of  a  body  1°C.,  is  called  its  capacity  for  heat. 

§  141.  Specific  heat  defined.  —  It  is  a  great  convenience 
to  be  able  to  compare  the  capacities  of  different  substances  for 
heat.  The  standard  employed  is  water,  and  the  ratio  which 
expresses  the  comparison  is  called  specific  heat. 

The  specific  heat  of  a  body  is  the  ratio  of  its  capacity  for  heat 
to  that  of  an  equal  weight  of  water. 

From  the  data  obtained  in  the  last  experiment  we  may  calcu- 
late the  specific  heat  of  lead  as  follows  :  The  same  quantity  of 
heat  that  raises  the  water  3.3°  (from  0°  to  3.3°)  raises  the  lead 
96.70°  (from  3.3°  to  100°)  ;  hence,  to  raise  the  lead  1°  requires 

3  3 

—^—=.034+  as  much  heat  as  to  raise  the  water  1°. 
96.7 

The  specific  heat  of  all  solids  and  liquids,  and  most  gases, 
increases  slightly  with  the  temperature.  Thus  water  at  0°  C.  has 


172          MOLECULAR  ENERGY.  —  HEAT. 

a  specific  heat  of  1  ;  at  40°,  1.0013  ;  at  80°,  1.0035.  Substances 
in  the  liquid  state  usually  have  a  higher  specific  heat  than  in  the 
solid  or  gaseous  state.  Thus  water  has  nearly  double  the 
specific  heat  of  ice,  and  a  little  more  than  double  the  specific 
heat  of  steam. 

REFERENCE   TABLES. 

Table  of  mean  specific  heat  between  0°  C.  and  100°  C. 
Hydrogen 3.4090 


Air 2375 

Sulphur 2026 

Glass  . .  .1770 


Iron 1138 

Copper 0952 

Mercury 0333 

Lead  . .  .  .0314 


Specific  heat  of  the  same  substance  in  different  states. 

Solid.  Liquid.  Gaseous. 

Water 5040     1.0000      4805 

Bromine 0833     1060       0555 

Lead 0314     0402      

Alcohol 5S-.77 45 

§  142.  One  cause  of  difference  in  capacity  for  heat.  — 
Of  the  whole  quantity  of  heat  applied  to  a  solid  or  liquid  bod}', 
only  a  part  goes  to  increase  the  heat  of  the  body,  and  thereby 
to  raise  its  temperature  ;  the  remainder  performs  interior  work. 
in  overcoming  cohesion  between  the  molecules  of  the  body,  and 
in  forcing  them  to  take  up  new  positions.  (Since,  then,  some 
of  the  heat  is  converted  into  potential  energy,  we  may  properly 
introduce  the  subject  of  specific  heat  at  this  place.)  The 
greater  the  portion  of  heat  consumed  in  interior  work  upon  :. 
body,  the  less  there  is  left  to  raise  its  temperature,  and  conse- 
quently the  greater  its  capacity  for  heat.  Thus,  when  equal 
quantities  of  heat  are  applied  to  equal  masses  of  water  and  lead, 
more  is  consumed  (i.e.,  converted  in  potential  energy)  in  interior 
work  upon  the  water  than  upon  the  lead  ;  consequently  the  tem- 
perature of  the  former  is  not  raised  as  much  as  that  of  the 
latter.  The  limits  of  this  work  forbid  the  discussion  of  the 
causes  of  the  difference  of  capacity  for  heat  of  different  gases. 


QUESTIONS    AND    PROBLEMS.  173 

§  143.  Great  capacity  of  water  for  heat.  —  Water  requires 
more  heat  to  warm  it,  and  gives  out  more  in  cooling  through  a 
given  range  of  temperature,  than  any  substance  except  hydrogen. 
The  quantity  of  heat  that  raises  a  kilogram  of  water  from  0° 
to  100°  C.  would  raise  a  kilogram  of  iron  from  0°  to  800°  or 
900° C.,  or  above  a  red  heat:  Conversely,  a  kilogram  of  water 
in  cooling  from  100°  to  0°C.  gives  out  as  much  heat  as  a  kilo- 
gram of  iron  in  cooling  from  about  900°  to  0°  C. 

QUESTIONS  AND  PROBLEMS. 

1.  How  much  heat  is  required  to  change  100k  of  ice  at  0°  into  steam 
at  100°  C.? 

2.  (a)  1000k  of  steam  at  100°  C.  is  conveyed  by  pipes  through  a 
building,  and  the  water  resulting  from  its  condensation  returns  to  the 
boiler  at  a  temperature  of  80°;  how  much  heat  is  given  out  in  the  build- 
ing.    (6)  The  same  quantity  of  heat  would  raise  how  many  kilograms 
of  water  from  0°  to  100°  ? 

3.  50k  of  water  at  100°  will  melt  how  many  pounds  of  ice  at  0°  C.  ? 

4.  How  much  heat  is  required  to  raise  lk  of  ice  from  — 10°  to  10°  C.? 

5.  (a)  Apply  the  same  quantity  of  heat  to  equal  weights  of  ice  and 
water,  each  at  a  temperature  of  0°  C. ;    when  the  latter  reaches  the 
boiling  point  what  will  be  the  temperature  of  the  former  ?     (&)  Why 
will  not  both  have  the  same  temperature  ? 

6.  What  effect  on  the  temperature  of  the  air  has  the  freezing  of  the 
water  of  lakes  and  other  bodies  of  water  ? 

7.  If  lk  of  iron  at  100°  is  immersed  in  lk  of  water  at  0°  C.,  what  will 
be  the  resulting  temperature  ? 

8.  What  is  the  specific  heat  of  a  substance,  lk  of  which  at  100°,  when 
put  into  lk  of  water,  at  0°  raises  its  temperature  to  5°  C.  ? 

9.  50k  of  mercury  at  80°  will  melt  what  weight  of  ice  at  0°  C.  ? 

10.  Why  is  hot  water  in  bottles  often  used  to  warm  beds  in  prefer- 
ence to  other  substances  ? 

11.  If  there  were  no  water  on  the  earth,  why  would  the  difference 
in  temperature  between  day  and  night,  and  between  summer  and  win- 
ter, far  exceed  what  it  is  now  ? 

12.  Why  are  places  in  vicinity  of  water  less  subject  to  extremes  of 
heat  and  cold  than  places  inland  ? 


174  MOLECULAR   ENERGY. HEAT. 


XXV.     THERMODYNAMICS. 

§  144.  Thermo-Dynamics  defined.  —  Thermo-dynamics  is 
that  branch  of  science  that  treats  of  the  relation  between  heat  and 
mechanical  work.  One  of  the  most  important  discoveries  in 
science  is  that  of  the  equivalence  of  heat  and  work;  that  is,  that 
a  definite  quantity  of  mechanical  work  can  always  produce  a 
definite  quantity  of  heat;  and  conversely,  this  heat,  if  the  conver- 
sion were  complete,  can  perform  the  original  quantity  of  work. 

§  145.  Correlation  and  conservation  of  energy.  —  The 
proof  of  the  facts  just  stated  was  one  of  the  most  important 
steps  in  the  establishment  of  the  grand  twin  conceptions  of 
modern  science.  (1)  That  all  kinds  of  energy  are  so  related  to 
one  another  that  energy  of  any  kind  can  be  changed  into  energy  of 
any  other  kind,  —  known  as  the  doctrine  of  CORRELATION  OF 
ENERGY  ;  (2)  That  when  one  form  of  energy  disappears,  an 
exact  equivalent  of  another  form  always  takes  its  place,  so  that 
the  sum  total  of  energy  is  unchanged,  —  known  as  the  doctrine 
of  CONSERVATION  OP  ENERGY.  These  two  principles  constitute 
the  corner-stone  of  physical  science. 

§  146.  Joule's  experiment.  —  The  experiment  to  ascertain 
the  "  mechanical  value  of  heat,"  as  performed  by  Dr.  Joule  of 
England,  was  conducted  about  as  follows.  He  caused  a  paddle- 
wheel  to  revolve  in  water  by  means  of  a  falling  weight  attached 
to  a  cord  wound  around  the  axle  of  a  wheel.  The  resistance 
offered  by  the  water  to  the  motion  of  the  paddles  was  the  means 
by  which  the  mechanical  motion  of  the  weight  was  converted 
into  heat,  which  raised  the  temperature  of  the  water.  Taking 
a  body  of  a  known  weight,  e.g.,  80k,  he  raised  it  a  measured 
distance,  e.g.,  53m  high;  by  so  doing  4240kgm  of  work  were 
performed  upon  it,  and  consequently  an  equivalent  amount  of 
energy  was  stored  up  in  it  ready  to  be  converted,  first,  into 
mechanical  motion,  then  into  heat.  He  took  a  definite  weight 


THE   STEAM   ENGINE.  175 

of  water  to  be  agitated,  e.g.,  2k,  at  a  temperature  of  0°  C. 
After  the  descent  of  the  weight,  the  water  was  found  to  have 
a  temperature  of  5°  C.  ;  consequently  the  2k  of  water  must  have 
received  10  units  of  heat  (careful  allowance  being  made  for 
all  losses  of  heat) ,  which  is  the  amount  of  heat-energy  that  is 
equivalent  to  4240kgm  of  work,  or  1  unit  of  heat  is  equivalent 
to  424kffm  of  work  (more  accurately  4i;3.98okgl"y . 

§  147.  Mechanical  equivalent  of  heat.  —  As  a  converse 
of  the  above  it  may  be  demonstrated  by  actual  experiment  that 
the  quantity  of  heat  required  to  raise  lk  of  water  from  0°  to 
1°  C.  will,  if  converted  into  work,  raise  a  424k  weight  lm  high, 
or  lk  weight  424m  high.  According  to  the  English  system,  the 
same  fact  is  stated  as  follows :  The  quantity  of  heat  that  will 
raise  1  Ib.  of  water  1°  F.  will  raise  772  Ibs.  1  ft.  high.  The 
quantity,  424kgm,  or  772  ft.  Ibs.,  is  called  the  mechanical  equiva- 
lent of  heat,  or  Joule's  equivalent  (abbreviated,  simply  J.). 

XXVI.     STEAM  ENGINE. 

§  148.  Description  of  a  steam  engine. — A  steam  engine 
is  a  machine  in  which  the  elastic  force  of  steam  is  the  motive 
power.  Inasmuch  as  the  elastic  force  of  steam  is  entirely  due 
to  heat,  the  steam  engine  is  properly  one  form  of  a  heat  engine; 
that  is,  it  is  a  machine  by  means  of  which  heat  is  continuously 
transformed  into  work  or  mechanical  motion. 

The  modern  steam  engine  consists  essentially  of  an  arrange- 
ment by  which  steam  from  a  boiler  is  conducted  to  both  sides 
of  a  piston  alternately  ;  and  then,  having  done  its  work  in  driv- 
ing the  piston  to  or  fro,  is  discharged  from  both  sides  alter- 
nately, either  into  the  air  or  into  a  condenser.  The  diagram  in 
Figure  119  will  serve  to  illustrate  the  general  features  and  the 
operation  of  a  steam  engine.  The  details  of  the  various 
mechanical  contrivances  are  purposely  omitted,  so  as  to  present 
the  engine  as  nearly  as  possible  in  its  simplicity. 


1T6 


MOLECULAR  ENERGY.  —  HEAT. 


In  the  diagram.  B  represents  the  boiler,  F  the  furnace,  S  the  steam 
pipe  through  which  steam  passes  from  the  boiler  to  a  small  chamber 
VC,  called  the  -calve  chest.  In  this  chamber  is  a  slide  valve  V,  which,  as 
it  is  moved  to  and  fro,  opens  and  closes  alternately  the  passages  M 
and  N  leading  from  the  valve  chest  to  the  cylinder  C,  and  thus  admits 
the  steam  alternately  each  side  of  the  piston  P.  When  one  of  these 
passages  is  open  the  other  is  always  closed.  Though  the  passage 
between  the  valve  chest  and  the  space  in  the  cylinder  on  one  side  of 


Fig.  119. 


the  piston  is  closed,  thereby  preventing  the  entrance  of  steam  into  this 
space,  the  passage  leading  from  the  same  space  is  open  through  the 
interior  of  the  valve  so  that  steam  can  escape  from  this  space  through 
the  exhaust  pipe  E.  Thus,  in  the  position  of  the  valve  represented  in 
the  diagram,  the  passage  N  is  open,  and  steam  entering  the  cylinder 
at  the  top  drives  the  piston  in  the  direction  indicated  by  the  arrow.  At 
the  same  time  the  steam  on  the  other  side  of  the  piston  escapes  through 
the  passage  M  and  the  exhaust  pipe  E.  While  the  piston  moves  to  the 
left,  the  valve  moves  to  the  right,  and  eventually  closes  the  passage 


THE    STEAM    ENGINE.  177 

N  leading  from  the  valve  chest,  and  opens  the  passage  M  into  the  same, 
and  thus  the  order  of  things  is  reversed. 

Motion  is  communicated  by  the  piston  through  the  piston  rod  R  to 
the  crank  G,  and  by  this  means  the  shaft  A  is  rotated.  Connected  with 
the  shaft  by  means  of  the  crank  H,  is  a  rod  R'  which  connects  with  the 
valve  V,  so  that  as  the  shaft  rotates,  the  valve  is  made  to  slide  to  and 
fro,  and  always  in  the  opposite  direction  to  that  of  the  motion  of  the 
piston. 

The  shaft  carries  a,  fly-wheel  W.  This  is  a  large,  heavy  wheel,  having 
the  larger  portion  of  its  weight  located  near  its  circumference;  it 
serves  as  a  reservoir  of  energy  which  is  needed  to  carry  the  shaft  past 
two  points  (called  the  dead  points)  in  each  revolution  of  the  shaft,  where 
the  power  communicated  directly  by  the  steam  is  ineffectual  in  moving 
the  shaft.  It  also  assists  to  make  the  rotation  of  the  shaft  and  all  other 
machinery  connected  with  it  uniform,  so  that  sudden  changes  of  velo- 
city resulting  from  sudden  changes  of  the  driving  power  or  resistances 
are  avoided.  (Why  should  the  wheel  be  heavy?  Why  should  it  be  large? 
Why  should  the  rim  be  heavy  ?  See  p.  102.)  By  means  of  a  belt  pass- 
ing over  the  wheel  W'  motion  may  be  communicated  from  the  shaft 
to  any  machinery  desirable. 

§  149.  Condensing  and  non-condensing  engines.1  — 
Sometimes  steam,  after  it  has  done  its  work  in  the  cylinder,  is 
conducted  through  the  exhaust  pipe  to  a  chamber  Q  called  a 
condenser,  where,  by  means  of  a  spray  of  cold  water  introduced 
through  a  pipe  T,  it  is  suddenly  condensed.  This  water  and  the 
condensed  steam  must  be  pumped  out  of  the  condenser  by  a 
special  pump  called  technically  the  air-pump;  thus  a  partial 
vacuum  is  maintained  t  Such  an  engine  is  'called  a  condensing 
engine.  The  advantage  of  such  an  engine  is  obvious,  for,  if  the 
exhaust  pipe,  instead  of  opening  into  a  condenser,  communicates 
with  the  outside  air  as  in  the  non-condensing  engine,  the  steam 
is  obliged  to  move  the  piston  constantly  against  a  resistance 
arising  from  atmospheric  pressure  of  15  pounds  for  every  square 
inch  of  the  surface  of  the  piston.  But  in  the  condensing  engine  no 
resistance  arises  from  atmospheric  pressure,  and  so  with  a  given 

1  The  terms,  low  pressure  and  high  pressure  engines,  are  not  distinctive  as  applied 
to  engines  of  the  present  day. 


178  MOLECULAR   ENERGY.  —  HEAT. 

steam  pressure  in  the  boiler  the  effective  pressure  on  the  piston 
is  considerably  increased  ;  hence,  condensing  engines  are  usually 
more  economical  in  their  working. 

§  150.  The  locomotive.  —  The  distinctive  feature  of  the  loco- 
motive engine  is  its  great  steam-generating  capacity,  considering  its 
size  and  weight,  which  are  necessarily  limited.  To  do  the  work  ordi- 
narily required  of  it,  from  three  to  six  tons  of  water  must  be  converted 
-into  steam  per  hour.  This  is  accomplished  in  two  ways:  viz.,  first,  by 
a  rapid  combustion  of  fuel  (from  a  quarter  of  a  ton  to  a  ton  of  coal 
per  hour);  second,  by  bringing  the  water  in  contact  with  a  large 
extent  (about  800  sq.  ft.)  of  heated  surface.  The  fire  in  the  "  fire-box  " 
A  (see  cut  on  the  opposite  page)  is  made  to  burn  briskly  by  means  of  a 
powerful  draft  which  is  created  in  the  following  manner :  The  exhaust 
steam,  after  it  has  done  its  work  in  the  cylinders  B,  is  conducted  by  the 
exhaust  pipe  C  to  the  smoke  box  D,  just  beneath  the  smoke  stack  E. 
The  steam  as  it  escapes  from  the  blast  pipe  F  pushes  the  air  above  it, 
and  drags  by  friction  the  air  around  it,  and  thus  produces  a  partial 
vacuum  in  the  smoke  box.  The  external  pressure  of  the  atmosphere 
then  forces  the  air  through  the  furnace  grate  and  hot-air  tubes  G,  and 
thus  causes  a  constant  draft.  The  large  extent  of  heated  surface  is 
secured  as  follows  :  The  water  of  the  boiler  is  brought  not  only  in  con- 
tact with  the  heated  surface  of  the  fire  box,  but  it  surrounds  the  pipes 
G  (a  boiler  usually  contains  about  150).  These  pipes  are  kept  hot  by 
the  heated  gases  and  smoke,  all  of  which  must  pass  through  them  to 
the  smoke  box  and  smoke  stack. 

Study  the  cut  carefully,  trace  the  course  of  the  steam  from  the  boiler 
H  through  the  throttle  valve  I  (under  the  control  of  the  engineer), 
steam  pipe  J,  etc.,  to  its  exit  from  the  smoke  stack.  Ask  some  engi- 
neer to  explain  from  the  object  the  offices  of  such  parts  as  you  do  not 
understand. 

The  steam  engine,  with  all  its  merits  and  with  all  the  improve- 
ments which  modern  mechanical  art  has  devised,  is  to-day  an 
exceedingly  wasteful  machine.  The  best  engine  that  has  been 
constructed  utilizes  only  twenty  per  cent  of  the  heat-power 
used. 


.« 


CHAPTER   IV. 
ELECTRICITY    AND    MAGNETISM. 

THERE  is  a  large  and  important  class  of  phenomena  depending 
on  new  principles  that  we  have  now  to  study ;  among  these  are 
lightning,  the  actions  of  telegraph  instruments,  the  electric  light, 
magnetic  attraction  and  repulsion,  etc.  We  shall  inquire  whether 
energy  is  involved  in  these  actions  as  in  all  those  we  have  so  far 
studied  ;  and,  if  so,  where  it  comes  from,  and  under  what  laws  it 
acts,  and  what  finally  becomes  of  it. 

If  we  chose  to  begin  with  those  experiments  easiest  to  per- 
form, we  should  take  those  with  magnets,  and  some  of  those  to 
be  studied  under  the  head  of  Frictional  Electricity ;  but  we 
should  find  it  difficult  to  see  clearly  how  the  subject  of  energy 
was  to  be  introduced.  So  let  us  take  first  some  experiments 
that  will  lead  us  more  easily  to  this  great  central  idea. 

XXVII.     CURRENT    ELECTRICITY. 

§  151.  Introductory  experiments.  —  Experiment  1.  Take 
a  strip  of  sheet  copper  and  a  strip  of  sheet  zinc,  each  about  10cm  long 
and  4cm  wide.  Take  also  a  tumbler  two-thirds  full  of 
water,  and  to  it  add  about  two  tablespoonfuls  of -sul- 
phuric acid.  Place  the  zinc  strip  in  the  liquid ;  in- 
stantly bubbles  of  gas  collect  on  the  surface  of  the 
zinc,  break  away  from  it,  rise  to  the  surface  of  the 
liquid,  and  are  rapidly  replaced  by  others.  These  are 
bubbles  of  hydrogen  gas,  and  may  be  collected  and 
burned.  It  is  soon  found  that  the  zinc  wastes  away, 
or  is  dissolved  in  the  liquid. 

Experiment  2.  Place  the  copper  strip  in  the  liquid 
a  little  way  from  the  zinc,  but  nowhere  touching  it;  no  bubbles  are 
formed.  Now  bring  the  extremities  of  the  two  strips  that  project  from 
the  liquid  into  contact,  as  in  Figure  120 ;  quickly  a  change  takes  place ; 


180  ELECTRICITY  AND  MAGNETISM. 

torrents  of  bubbles  now  rise  from  the  copper,  and  only  a  very  few 
from  the  zinc;  still  it  is  found,  after  a  lapse  of  time,  that  the  copper 
has  undergone  no  change,  while  the  zinc  has  wasted  away. 

Experiment  3.  Withdraw  the  zinc  from  the  liquid,  and  while  it  is 
yet  wet  rub  a  little  mercury  over  its  surface,  so  that  it  may  become 
completely  wet  with  the  liquid  metal.  Now  repeat  the  above  experi- 
ments in  order.  First,  it  is  found  that  the  zinc,  when  alone  in  the 
liquid,  is  not  affected  by  it,  and  no  bubbles  of  gas  are  formed.  But 
when  the  two  metals  are  immersed  in  the  liquid,  and  are  brought  into 
contact,  bubbles  of  gas  quickly  appear  on  the  copper  as  before,  but 
none  appear  on  the  zinc,  although  the  zinc  is  still  the  metal  that  wastes 
away,  while  the  copper  remains  unchanged. 

Experiment  4.  Instead  of  placing  the  metals  in  contact,  connect 
them  by  means  of  a  wire  of  any  metal,  the  points  of  contact  being 
clean ;  the  bubbles  are  given  off  at  the  copper  as  before.  Cut  the  con- 
necting wire  at  any  point,  or  separate  it  from  the  zinc  or  copper ;  all 
evolution  of  bubbles  ceases,  but  begins  again  the  instant  the  contact  is 
made. 

Experiment  5.  Interpose  between  the  connecting  wire  and  the 
plates,  or  between  the  cut  ends  of  the  wire,  a  piece  of  paper,  wood,  or 
rubber,  or  use  some  one  of  these,  instead  of  a  wire,  to  connect  the  two 
plates ;  no  action  appears  in  the  cell. 

Thus  it  appears  that  there  must  be  a  connection,  and  that  too 
of  a  particular  kind,  between  the  two  metals,  in  order  that 
action  may  occur.  The  connecting  wire,  then,  is  an  important 
factor  in  the  changes  that  occur,  and  it  seems  altogether  prob- 
able that  some  influence  is  exerted  by  the  metals  upon  one 
another  through  the  wire ;  in  other  words,  that  something 
unusual  is  going  on  in  the  wire  when  so  used. 

Does  the  connecting  wire  possess  any  unusual  properties  dur- 
ing this  use  ? 

Experiment  6.  Take  an  ordinary  compass,  or  poise  a  magnetic 
needle  at  its  center,  either  by  a  pivot,  as  in  Figure  121,  or  by  a  fine, 
untwisted  silk  thread,  and  arrange  the  connecting  wires  as  in  the  figure. 
The  needle,  when  at  rest,  points  north  and  south.  The  connecting 
wire  being  over  the  needle,  and  parallel  with  it,  bring  the  two  extremi- 
ties of  the  wire  into  contact;  instantly  the  needle  turns  on  its  axis, 
tending  to  place  itself  at  right  angles  to  the  wire,  and,  after  a  few 


INTRODUCTORY  EXPERIMENTS. 


181 


Fig.  121. 


vibrations,  takes  up  a  permanent  position,  forming  an  angle  with  the 
wire.  This  deviation  from  its  normal  position  is  called  a  deflection  of 
the  needle.  Separate  the  two  extremities  of  the  wires  ;  the  needle 
swings  back  to  its  normal  position. 

Experiment  7.  Bring  the  ends  of  the  wires  together  as  before, 
interposing  a  piece  of  paper  be- 
tween them;  the  needle  is  not 
moved.  This  is  another  illus- 
tration of  the  necessity  of  em- 
ploying a  suitable  substance  for 
a  connector  in  order  that  any 
action  may  take  place. 

Experiment  8.  Take  a  large 
iron  nail,  and  plunge  one  end  of 
it  into  iron  filings,  and  then  re- 
move it ;  no  filings  cling  to  the 
nail.  Next,  wrap  a  piece  of  pa- 
per around  the  nail,  leaving  the 

ends  exposed,  and  wind  around  it  20  or  more  turns  of  copper  wire, 
taking  pains  that  the  coils  do  not  touch  each  other.  Now  connect  the 
wire  with  the  zinc  and  copper  just  used,  so  that  there  will  be  a  con- 
tinuous connection  from  one  strip  to  the  other  through  the  coil,  and 
dip  one  end  of  the  nail  again  into  the  filings ;  raise  the  nail,  and  a 
considerable  quantity  of  filings  cling  to  the  nail. 

From  these  experiments,  and  others  which  will  be  performed 
later,  it  appears  that  when  the  zinc  and  copper  are  thus  placed 
in  acid  and  connected  by  a  wire,  the  wire  exhibits  unusual  prop- 
erties. The  cause  of  these  and  many  other  allied  phenomena 
is  called  electricity,  and  these  properties  in  the  wire  are  attributed 
to  the  passage  of  an  electric  current  through  it. 

Almost  from  the  dawn  of  the  science  of  electricity  there  have 
been  many  who  have  believed  in  the  existence  of  an  "  electric 
fluid  "  ;  but  it  is  not  yet  claimed  that  there  is  any  positive  proof 
of  its  existence,  and  therefore  we  cannot  affirm  that  a  current 
passes  through  the  wire.  Yet  the  theory  upon  which  these 
terms  are  based  is  at  least  a  convenient  one  by  which  to  explain 
the  various  phenomena,  and  the  terms  are  therefore  universally 
used. 


182  ELECTRICITY   AND   MAGNETISM. 

§  152.  Some  definitions.  —  Experiments  (not  easily  per- 
formed by  the  pupil)  show  that  the  current  traverses  the  liquid 
between  the  metallic  plates  in  the  battery  at  the  same  time  that 
it  traverses  the  connecting  wire,  so  that  the  current  makes  a 
complete  circuit.  The  term  circuit  is  applied  to  the  entire  path 
along  which  electricity  is  supposed  to  flow,  and  the  wire  along 
which  it  flows  is  called  the  conductor.  Bringing  the  two  extremi- 
ties of  the  wires  in  contact,  and  separating  them,  is  called,  tech- 
nically, making  and  breaking,  or  closing  and  opening,  the  circuit. 

Our  arrangement  of  acidulated  water  and  two  metals  is  called 
a  voltaic1  cell,  element,  or  pair.  A  series  of  cells,  properly  con- 
nected, is  called  a  battery,  though  this  term  is  sometimes  applied 
to  a  single  cell. 

§  153.  Direction  of  the  current.  —  It  is  evidently  neces- 
sary, in  defining  a  current,  to  know  its  direction  ;  but  a«  no 

Fig.  122.  Fig.  123. 


phenomena  known  serve  to  indicate  the  direction,  electricians 
have  universally  agreed  to  assume  that  in  such  a  cell  as  described 
the  electricity  flows  from  the  copper  to  the  zinc  in  the  wire. 

Experiment.  Place  the  conducting  wire  over  and  parallel  with  a 
magnetic  needle,  in  the  manner  represented  in  Figure  122;  the  north 
end  of  the  needle  is  deflected  toward  the  west.  Turn  the  cell  half-way 
around  so  as  to  have  the  position  in  Figure  123;  a  deflection  of  the 
needle  toward  the  east  shows  that  the  current  is  reversed. 

1  Voltaic,  from  Volta,  au  Italian,  who  devised  the  voltaic  pile,  which  is  the  parent 
of  all  batteries. 


POTENTIAL.  183 

§154.  Poles  or  electrodes. — The  copper  strip  is  fre- 
quently called  the  negative  plate,  and  the  zinc  strip  the  positive 
plate,  and  the  end  of  any  conductor  connected  with  the  copper 
or  negative  plate  is  called  the  positive  pole,  or  electrode,  while 
the  end  connected  with  the  zinc  or  positive  plate  is  called  the 
negative  pole,  or  electrode.  Then,  by  our  assumption,  if  we  bring 
together  the  -\-  and  —  electrodes,  the  current  passes  from  the 
former  to  the  latter,  across  the  junction  ;  and  generally  that  plate 
and  that  electrode  is  -f-  from  which  the  current  goes,  and  that 
plate  and  that  electrode  is  —  to  which  the  current  goes. 

V  §  155.  Potential.  —  If  a  current  of  water  is  to  flow  from 
one  vessel  A  to  another  B  through  a  pipe,  we  know  that  there 
must  be  a  greater  pressure  at  the  end  of  the  pipe  next  A  than 
at  the  other  end ;  i.e.,  in  ordinary  language,  the  head  of  water 
in  A  is  higher  than  in  B.  So  in  the  study  of  electricity  we  find 
two  bodies  in  different  conditions  such  that  a  current  of  elec- 
tricity flows  from  one  (A)  to  the  other  (B) ,  and  we  say  that  A  has 
a  higher  potential  than  B.  In  the  experiments  already  tried  the 
+ electrode,  or  the  wire  connected  with  the  copper,  has  a  higher 
potential  (according  to  our  assumption  for  the  direction  of  the 
current)  than  the  —electrode  or  the  wire  connected  with  the 
zinc. 

It  is  not  necessary  that  we  know  the  hight  from  the  center  of 
the  earth,  or  above  the  level  of  the  sea,  of  a  reservoir,  and  the 
tank  it  is  to  fill ;  what  we  want  to  know  is  the  difference  in 
hight  between  the  two.  Just  so  it  is  difference  of  potential 
that  determines  the  direction  of  the  flow,  and  the  quantity  of 
electricity  that  is  to  flow  through  a  given  conductor  in  a  given 
time.  Sometimes  the  potential  of  a  body  is  expressed  as  so 
many  units  above  or  below  that  of  the  earth,  assumed  as 
zero. 

§  156.  Ampere's  rule  for  determining  deflection,  etc.  — 
If  the  magnetic  needle  is  placed  over  the  current,  its  deflection 


184  ELECTRICITY  AND  MAGNETISM. 

is  the  reverse  of  that  produced  when  placed  beneath  it.     This 
tends  to  confuse ;  but  an  artifice,  proposed  by  Ampere,  will 
readily  enable  us  to  determine  the  deflection,  when  the  direction 
Fig.  124.  °f  tne  current  is  known,  and  to  deter- 

mine  the  direction  of  the  current  when 
that  of  the  deflection  is  known.  He 
suggests  that  we  imagine  ourselves  to  be 
swimming  in  the  current,  and  with  the 
current,  and  facing  the  needle;  in  which 
case  the  north  end  of  the  needle  will 
always  be  deflected  towards  our  left. 
(The  pupil  should  test  this  rule  experi- 
mentally in  various  ways  and  many  times,  till  he  is  familiar  with 
its  application.) 

§  157.  Galvanoscope.  —  The  magnetic  needle  serves  the 
double  purpose  of  determining  both  the  presence  and  direction  of 
a  current  in  a  wire.  A  needle  used  for  these  purposes  is  called 
a  galvanoscope.1  Electricity  set  in  motion  by  a  voltaic  battery 
is  called  galvanic  or  voltaic  and  sometimes  current  electricity. 

EXERCISES. 

1.  Let  the  current  be  above  the  needle,  and  go  from  N  to  S ;  what 
will  be  its  deflection? 

2.  Let  the  current  be  below  the  needle,  and  go  from  S  to  N ;  what 
deflection  will  it  cause? 

3.  Let  the  needle  be  above  the  current ;  what  must  be  the  direction 
of  the  current  when  the  north  end  is  deflected  to  the  east? 

4.  Let  the  needle  be  below  the  current,  and  the  deflection  toward  the 
east;  what  is  the  direction  of  the  current? 

5.  What  is  the  effect  when  the  current  is  at  the  side  of  the  needle? 

V  §  158.  How  electric  energy  originates.  —  If  you  take  the 
liquid  from  a  battery  after  considerable  zinc  has  disappeared  in  it, 
and  evaporate  it,  there  will  crystallize  out  of  it  a  white,  transparent 

1  Galvanoscope,  named  for  Oalvani,  one  of  the  early  discoverers  in  electricity. 


WHY   THE   HYDROGEN   APPEARS,    ETC.  185 

solid  in  needle-like  crystals.  This  substance  is  a  compound  of 
zinc  and  sulphuric  acid,  and  is  called  zinc  sulphate.  The  solu- 
tion of  the  zinc  is  the  result  of  a  chemical  action  between  the 
zinc  and  the  acid.  Hydrogen  is  another  product  of  the  action. 
The  water  serves  as  a  solvent  of  the  zinc  sulphate.  The  chemist 
symbolizes  sulphuric  acid  thus,  H2SO4;  zinc,  Zn.  He  describes 
the  change  that  occurs  by  saying  that  the  zinc  replaces  the 
hydrogen  H2  in  the  acid  (in  other  words,  the  hydrogen  is  set 
free  from  the  combination) ,  while  the  SO4  part  of  the  acid  unites 
with  the  zinc,  and  forms  zinc  sulphate,  ZnSO4.  But  we  have 
also  discovered  another  important  result  of  the  operation; 
namely,  that  electric  energy  is  developed  by  the  chemical  action 
between  the  liquid  and  the  zinc. 

Is  the  electric  energy  created  out  of  nothing  ?  We  have  already 
become  familiar  with  the  fact  (§  105,  page  140)  that  chemical 
potential  energy  in  a  lump  of  coal  may  be  converted  into  kinetic 
energy,  as  is  constantly  done  in  the  steam  engine.  Similarly, 
we  might  burn  zinc  to  make  steam.  Coal  and  zinc,  then,  possess 
a  power  to  enter  into  new  combinations  ;  this  power  is  usually 
called  chemical  energy,  or  chemism.  It  exists  in  a  potential 
condition,  until  it  is  aroused  from  this  dormant  state  by  bring- 
ing together  suitable  substances.  When  chemical  energy  be- 
comes kinetic,  it  may  be  transformed  into  mechanical  energy, 
as  when  a  cannon-ball  is  set  in  motion  by  the  burning  of  gun- 
powder ;  or  it  may  be  changed  into  heat,  as  in  the  ordinary 
burning  of  fuel ;  or  into  both  heat  and  electric  energy,  as  in  the 
burning  of  zinc  in  the  battery. 

§  159.  Why  the  hydrogen  appears  at  the  copper  plate. 
—  When  zinc  dissolves  in  sulphuric  acid,  hydrogen  is  liberated, 
and  ordinarily  rises  at  once  in  bubbles  ;  but  in  the  voltaic  cell  it 
rises  from  the  copper,  yet  no  bubbles  are  seen  to  move  through 
the  liquid  between  the  plates.  As  a  plausible  but  imperfect  ex- 
planation of  these  phenomena,  the  well-known  hypothesis  of 
Grotthuss  was  offered.  It  assumes  what  many  chemists  believe, 


186  ELECTRICITY  AND   MAGNETISM. 

that  at  the  instant  that  a  substance  is  liberated  from  a  com- 
pound it  possesses  unusual  readiness  to  enter  into  combination 
with  other  molecules. 

Let  the  circles  1,  2,  3,  etc.  (Fig.  125),  represent  a  series  of 
molecules  of  H2SO4  connecting  the  two  plates.  At  the  instant 

the  circuit  is  closed 
the  SO4  of  molecule  1 
unites  with  a  molecule 
of  zinc,  setting  free 
its  H2 ;  this  instantly 
unites  with  the  SO4  of 
molecule  2,  forming  a 
new  molecule,  1',  of 
H2SO4,  and  setting 
free  the  H2  of  molecule 
2.  This  H2  unites  with 
the  SO4  of  molecule  3, 
forming  molecule  2f.  This  decomposition  and  recomposition 
continues  till  the  H2  of  molecule  6  is  set  free.  This  H2  unites 
with  other  molecules  of  h}*drogen,  and  finally  rises  in  a  bubble 
to  the  surface ;  so  the  molecule  of  hydrogen  that  escapes  is 
not  the  molecule  that  was  first  set  free  at  the  zinc  plate. 

§  160.  Electro-chemical  series.  —  If  two  plates  of  zinc 
were  used  in  a  cell,  instead  of  a  zinc  and  a  copper,  we  should 
nave  a  tendency  to  opposite  currents,  which  would  neutralize 
each  other ;  or,  stated  differently,  there  would  be  no  difference 
of  potential  between  the  .two  plates,  and  so  no  current.  It  is, 
therefore,  important  that  only  one  of  the  metals  should  be  acted 
upon.  TJie  greater  the  disparity  between  the  two  solid  elements, 
with  reference  to  the  action  of  the  liquid  on  them,  the  greater  the 
difference  in  potential;  hence,  the  greater  the  current.  In  the  fol- 
lowing electro-chemical  series  the  substances  are  so  arranged 
that  the  most  electro-positive,  or  those  most  affected  by  dilute 
sulphuric  acid,  are  at  the  beginning,  while  those  most  electro- 


IMPORTANCE   OF   AMALGAMATING  THE   ZINC.        187 

negative,  or  those  least  affected  by  the  acid,  are  at  the  end.    The 
arrow  indicates  the  direction  of  the  current  through  the  liquid. 


1    *     1     § 

+1    I    a    1    I  I    I    1 


It  will  be  seen  that  zinc  and  platinum  are  the  two  metals  best 
adapted  to  give  a  strong  current. 

The  essential  parts  of  any  galvanic  cell  in  the  ordinar}^  form 
are  a  liquid  and  two  different  solids,  one  of  which  is  more 
readily  acted  upon  chemically  by  the  liquid  than  the  other. 

§  161.  Importance  of  amalgamating  the  zinc.  —  All 
commercial  zinc  contains  impurities,  such  as  carbon,  iron,  etc. 
Figure  126  represents  a  zinc  element  having  on  its  surface  a 
particle  of  iron  a,  purposely  magnified.  If  such  a 
plate  is  immersed  in  dilute  sulphuric  acid,  the  par- 
ticles of  iron  with  the  zinc  will  form  numerous  voltaic 
circuits,  and  a  transfer  of  electricity  along  the  surface 
will  take  place.  This  coasting  trade,  as  it  were,  be- 
tween the  zinc  and  the  impurities  on  its  surface, 
diverts  so  much  from  the  regular  battery  current,  and 
thereby  weakens  it.  In  addition  to  this,  it  occasions 
a  great  waste  of  chemicals,  because,  when  the  regular 
circuit  is  broken,  this  local  action,  as  it  is  called,  still 
continues.  If  pure  zinc  were  available,  no  local  action  would 
occur  at  any  time,  and  there  would  be  no  consumption  of 
chemicals,  except  at  times  when  the  circuit  is  closed.  If 
mercury  is  rubbed  over  the  surface  of  the  zinc,  after  the  latter 
has  been  dipped  in  acid  to  clean  its  surface,  the  mercury  dis- 
solves a  portion  of  the  zinc,  forming  with  it  a  semi-liquid 
amalgam  which  covers  up  its  impurities,  and  the  amalgamated 
zinc  then  comports  itself  like  pure  zinc. 


188 


ELECTRICITY  AND   MAGNETISM. 


XXVIII.     VARIOUS    BATTERIES. 

§  162.  Polarization  of  plates.  —  When  the  zinc  and  cop- 
per elements  are  first  placed  in  the  dilute  acid,  a  very  good 
current  of  electricity  is  produced  ;  but  the  current  soon  becomes 
feeble.  The  cause  is  easily  discovered.  The  liberated  hydro- 
gen adheres  very  strongly  to  the  copper,  as  there  is  nothing  for 
it  to  unite  with  chemically  ;  and  therefore  the  plate  is  very  soon 
visibly  covered  with  bubbles,  which  may  be  scraped  off  with  a 
feather  or  swab,  but  only  to  have  the  same  thing  repeated.  This 
coating  of  bubbles  impedes,  to  a  considerable  extent,  the  flow 
of  electricity,  and  diminishes  the  current.  Besides,  a  plate 
coated  with  hydrogen  is  more  strongly  electro-positive  than  usual, 
and  so,  as  the  coating  slowly  forms,  the  difference  of  potential 
between  the  two  plates  becomes  less  and  less ;  the  current, 
therefore,  must  become  weaker  and  weaker  as  the  coating  thick- 
rig.  127.  ens-  This  action  is  usually  called  polariza- 
tion of  the  plates.  Very  many  methods  have 
been  devised  for  remedying  these  evils.  The}' 
are  all  included  in  two  classes :  mechanical 
and  chemical  methods. 


§  163.  Smee  battery.  —  The  Smee  bat- 
tery (Fig.  127)  is  an  example  of  the  former 
class.  A  silver  plate,  or  sometimes  a  lead 
plate,  is  coated  with  a  fine,  powdery  deposit 
of  platinum,  which  gives  the  surface  a  rough 
character,  so  that  the  hydrogen  will  not 
readily  adhere  to  it.  Dilute  sulphuric  acid  is  used  in  this  bat- 
tery. This  plate  is  suspended  between  two  zinc  plates,  but  not  . 
allowed  to  touch  them. 

A  very  effective  battery  may  be  constructed  by  arranging  that 
the  copper  plate  may  revolve  in  the  liquid,  so  that  the  hydrogen 
may  be  removed  by  friction  between  the  plate  and  liquid.  But 
this  necessitates  a  constant  force  to  keep  the  plate  in  motion. 


GRENET  BATTERY. 


189 


No  mechanical  method  can  wholly  prevent  the  collection  of 
hydrogen  on  the  electro-negative  plate.  This  can  only  be  com- 
pletely accomplished  by  furnishing  some  chemical  with  which  the 
hydrogen,  as  soon  as  liberated,  may  go  into  combination. 

§  164.  Grenet  battery In  the 

Grenet  or  bottle  battery  the  hydrogen 
is  disposed  of  by  chemical  action. 
The  chemical  action  is  quite  complex, 
and  will  therefore  be  omitted.  The 
liquid  used  is  a  mixture  of  potassium 
bichromate  and  sulphuric  acid  dis- 
solved in  water.  The  zinc  plate  Z 
(Fig.  128)  is  suspended  between  two 
carbon  plates,  C,  C.  The  carbons 
remain  in  the  liquid  all  the  time. 
(Carbon  is  now  largely  used  in 
batteries  for  the  electro  -  negative 
plate.) 

This  battery  gives  a  very  energetic 

current  for  a  short  time,  but  the  liquid  soon  becomes  exhausted. 
It  is  a  very  convenient  battery,  as,  when  not  in  use,  we  have 
only  to  draw  the  zinc  out  of  the  liquid  by  the  brass  stem  a, 
and,  on  pushing  the  zinc  back  into  the  liquid,  action  commences 
immediately.  It  is  well  to  allow  the  battory  to  "  rest"  occa- 
sionally by  withdrawing  the  zinc  from  the  liquid  for  a  short  time. 
With  one  Grenet  cell  nearly  every  experiment  described  in  this 
book  can  be  performed. 

§  165.  Bunsen's  and  Grove's  batteries.  —  There  is, 
also,  besides  the  single-fluid  batteries,  a  large  number  of  two- 
fluid  batteries.  The  zinc  is  immersed  in  the  liquid  to  be  de- 
composed, which  most  frequently  is  dilute  sulphuric  acid,  and 
the  conducting  plate  is  surrounded  with  a  liquid  which  can  be 
decomposed  by  hydrogen.  The  two  liquids  are  usually  sep- 


190 


ELECTRICITY   AND   MAGNETISM. 


arated  by  a  porous  partition  of  nnglazed  earthenware,  which 
prevents  the  liquids  from  mingling,  except  very  slowly,  but  does 
not  prevent  the  passage  of  hydrogen  or  electricity.  Bunsen's 
batteiy  (Fig.  129)  has  a  bar  of  carbon  immersed  in  strong  nitric 
acid  contained  in  a  porous  cup.  This  cup  is  then  placed  in 
another  vessel  containing  the  dilute  sulphuric  acid ;  and  im- 
mersed in  the  same  liquid  is  a  hollow,  cylindrical  plate  of  zinc, 
which  nearly  surrounds  the  porous  cup.  The  hydrogen  trav- 
erses, by  composition  and  recomposition,  the  sulphuric  acid, 
passes  through  the  porous  partition,  and  immediately  enters  into 
chemical  action  with  the  nitric  acid,  so  that  none  reaches  the 

carbon.  There  are  produced  by 
this  action,  water  —  which  in  time  di- 
lutes the  acid  —  and  orange-colored 
fumes  of  nitric  oxide,  which  rise  from 
the  battery.  These  fumes  are  very 
offensive,  corrosive,  and  poisonous. 
If  the  nitric  acid  is  first  saturated 
with  nitrate  of  ammonium,  the  acid 
will  last  longer  without  dilution,  and 
the  fumes  are  almost  entirely  pre- 
vented. Strong  sulphuric  acid  will 
not  answer  in  any  battery.  Usually, 
to  one  part  of  sulphuric  acid  about  12 
parts  by  weight  or  20  by  volume  of  water  are  added  to  dissolve 
the  sulphate  of  zinc  formed. 

Grove  used  a  strip  of  platinum  instead  of  the  carbon  rod  in 
his  battery.  When  carbon  is  used  for  the  negative  plate,  a  so- 
lution of  bichromate  of  potassium  is  frequently  substituted  for 
nitric  acid,  and  thereby  the  disagreeable  fumes  are  avoided. 
Bunsen's  and  Grove's  batteries  are  unequalled  for  powerful 
and  constant  currents,  and  are  the  best  for  ordinary  lecture- 
room  experiments ;  but  they  require  frequent  attention,  and 
are  expensive,  so  that  they  are  little  used  for  work  of  long 
duration. 


GRAVITY   BATTERY. 


191 


Fig.  130. 


§  166.  Gravity  battery.  —  The  battery  principally  used  in 
this  country  for  telegraphing  is  called  the  gravity  battery.  A 
copper  plate  C,  Figure  130,  is 
placed  on  the  bottom  of  a  vessel 
and  covered  with  crystals  of  cop- 
per sulphate  (blue  vitriol),  and 
the  whole  covered  with  water. 
As  the  vitriol  dissolves,  its  spe- 
cific gravity  causes  it  to  remain 
at  the  bottom,  in  contact  with  the 
copper  plate.  The  zinc  plate  Z 
is  suspended  in  the  clear  liquid 
above.  To  start  the  action  quickly, 
a  teaspoonful  of  common  salt  or 
zinc  sulphate  is  dissolved  in  the 
water.  As  the  chemical  action 
proceeds,  the  vitriol  is  decom- 
posed, its  sulphuric  acid  constitu- 
ent unites  with  the  zinc,  forming  soluble  zinc  sulphate,  and  the 
copper  constituent  is  deposited  in  a  metallic  state  on  the  copper 
plate.  The  zinc  does  not  require  amalgamation. 

XXIX.  EFFECTS  PRODUCED  BY  ELECTRICITY. 

§  167.  Heating  effect.  —  Experiment  1.  Introduce  between 
the  electrodes  of  a  Bunsen  or  Grenet  cell  a  piece  of  platinum  wire  A, 
Figure  131,  about  6cm  long  and  in  size  about  No.  36.  The  platinum  wire 
becomes  white  hot. 

Experiment  2.  Stretch  the  platinum  wire  over  a  gas-burner,  turn 
on  the  gas,  and  light  it  by  the  heat  of  the  wire. 

Experiment  3.  Strew  lycopodium  powder  over  a  tuft  of  cotton-wool, 
and  ignite  it  with  the  heated  wire. 

Experiment  4.  Connect  the  battery  wires  (Fig.  131)  with  a  gal- 
vanometer (see  page  198)  G,  as  in  the  figure ;  the  needle  is  deflected. 
Remove  the  platinum  wire,  and  close  the  circuit ;  the  needle  is  deflected 
more  than  before. 

What  transformations  of  energy  took  place  in  the  above  ex- 
periments? 


192 


ELECTRICITY  AND   MAGNETISM. 


§  168.   Luminous  effect.  —  We  have  already  seen  one  illus- 
.  i3i.  tration  of  this  effect 

in  the  glowing  of  the 
white-hot  platinum 
wire. 

Experiment.  'Attach 
one  pole  of  the  battery 
to  a  file  (Fig.  132),  and 
pass  the  other  pole  over 
its  rough  surface.  The 
file  forms  part  of  the 
circuit ;  and  as  the  wire 
passes  over  it,  the  cir- 
cuit is  rapidly  made  and 
broken,  and  each  break 
causes  a  spark  at  the  point  where  the  circuit  is  broken.  The  shower 
of  sparks  that  flies  from  the  file  is  due  to  red-hot 

particles  of  iron  that 
are  projected  into  the 


Fig.  132. 


§  169.  Chemical 
effect.  —Experi- 
ment 1.  Steep  some 
leaves  of  purple  cab- 
bage; the  infusion  has  a  deep  purple  color.  Dis- 
solve a  little  caustic  soda,  and  pour  a  few  drops 
of  the  solution  into  a  portion  of  the  infusion,  and  the  purple  will  be 
changed  to  a  green.  Caustic  soda  is  an  alkali,  and  cabbage  infusion  is 
turned  green  only  by  alkalies.  Pour  a  few  drops  of  dilute  sulphuric  acid 
into  another  portion  of  the  infusion,  and  the  purple  will  be  changed  to  a 
red.  Only  acids  turn  purple  cabbage  infusions  rted.  Now  prepare  a  con- 
centrated solution  of  sodium  sulphate.  Color  the  solution  with  a  por- 
tion of  the  purple  cabbage  infusion,  and  partly  fill  a  V-shaped  glass  tube 
(Fig.  133)  with  this  liquid.  Employ  a  battery  of  two  Grove  or  Grenet 
cells  connected  in  series.  (See  p.  208.)  Attach  to  the  poles  of  the 
battery-wires  two  narrow  strips  of  platinum,  and  place  one  of  these 
strips  in  each  branch  of  the  tube,  a  little  way  apart,  so  that  the  current 
will  be  obliged  to  traverse  a  part  of  the  liquid.  Close  the  circuit; 
bubbles  of  gas  are  immediately  disengaged  from  the  platinum  strips ; 


CHEMICAL  EFFECT.  193 

soon  the  liquid  around  the  —pole  is  turned  green,  while  that  around 
the  +pole  is  turned  red.  Evidently  decomposition  of  the  sodium 
sulphate  has  taken  place ;  an  acid  and  an  alkali  are  the  results. 

The  current  which  is  maintained  by  chemical  action  in  the  bat- 
tery is  capable  of  doing  chemical  work  outside  the  battery.  A 
substance  that  may  be  decomposed  by  electricity  is  called  an 
electrolyte,  and  the  process  electrolysis.1  The  electrolyte  must  be 
a  compound  substance,  and  in  a  liquid  state,  either  by  solution 
or  fusion.  A  large  number  of  substances  are  composed,  like 
sodium  sulphate,  of  an  acid,  and  either  an  alkali  or  some  other 
substance  that  will  neutralize  an  acid.  Any  substance  that  will 
neutralize  an  acid  is  called  a  base,  and  a  compound  of  an  acid 
and  a  base  is  called  a  salt.  When  a  salt  is  electrolyzed,  the 
base  always  appears  at  the  —pole,  and  the  acid  at  the  -f-pole. 

Experiment  2.  Prepare  a  solution  of  the  salt  copper  sulphate, 
and  subject  it  to  electrolysis,  as  in  the  last  experiment;  copper  collects 
on  the  —platinum,  and  sulphuric  acid  and  oxygen  at  the  +platinum. 
Remove  the  platinum  strips,  and  introduce  the  copper  terminals ;  cop- 
per is  now  deposited  on  the  —pole  as  before,  but  the  -f  pole  wastes 
away. 

The  chemical  symbol  for  copper  sulphate  is  CuSO4.  By 
electrolysis  it  is  separated  into  Cu  and  SO4.  When  a  copper 
+pole  is  used,  the  SO4  immediately  unites  with  a  molecule  of 
the  copper  (Cu)  of  this  pole,  and  forms  a  new  molecule  of  cop- 
per sulphate  (CuSO4),  which  is  dissolved  by  the  water.  This 
accounts  for  the  wasting  away  of  the  +pole.  The  solution 
does  not  lose  its  strength,  for  as  fast  as  a  molecule  of  copper 
sulphate  is  decomposed,  another  is  formed.  But  when  platinum 
poles  are  used,  the  SO4  does  not  combine  with  the  platinum,  but 
enters  into  chemical  action  with  the  water.  The  SO4  combines 
with  the  hydrogen  of  the  water,  forming  sulphuric  acid,  and  the 
oxygen  of  the  water  is  set  free.  (SO4  +  H2  O  =  H2  SO4  +  O.) 

1  Electrolysis,  a  loosening  by  electricity. 


194  ELECTRICITY   AND   MAGNETISM. 

The  liberation  of  the  oxygen  is  the  result  of  a  secondary  chemi- 
cal action,  subsequent  to  the  electrolytic  action. 

Experiment  3.  Prepare  a  solution  of  tin  chloride,  by  dissolving 
scraps  of  granulated  tin  in  hot  hydrochloric  acid.  Add  a  little  water. 
Electrolyze  this  salt  in  solution,  using  platinum  poles.  A  beautiful 
growth  of  tin  crystals  will  shoot  out  from  the  —pole  and  spread 
towards  the  -f  pole,  bearing  a  strong  resemblance  to  vegetable  growth ; 
hence  it  is  called  the  "  tin  tree." 

In  a  similar  manner,  silver  and  lead  trees  may  be  prepared 
Fig.  134.  from  their  salts,  silver  nitrate  and 

lead  acetate.  Each  metal  has  its 
own  peculiar  form  of  growth  ;  and 
sometimes  the  same  metal,  par- 
ticularly silver,  exhibits  different 
forms,  according  to  the  strength 
of  the  solution  and  the  power  of 
the  current.  In  Figure  134,  A 
represents  a  silver  tree  deposited 
from  a  weak  solution  of  silver 
nitrate,  and  B  a  tree  formed  from 
a  still  weaker  solution  of  the 
same. 

Experiment  4.  Remove  the  bot- 
tom of  a  glass  bottle  haviug  a  wide 
mouth,  fit  a  cork  to  the  mouth,  and 
pass  two  insulated  wires  through  the 
cork,  terminating  in  platinum  strips  (Fig.  135).  Fill  two  test-tubes  antf 
part  of  the  inverted  bottle  with  dilute  sulphuric  acid,  and  invert  the 
tubes  over  the  platinum  poles.  The  circuit  is  thus  closed  through  the 
liquid.  Bubbles  of  gas  immediately  rise  from  the  poles  and  displace 
the  liquid  in  the  tubes.  About  twice  as  much  gas  collects  over  the 
—  pole  as  over  the  +pole.  Thrust  a  lighted  splinter  into  each  of  the 
gases  :  the  former  burns ;  the  latter  causes  the  splinter  to  burn  much 
more  rapidly  than  it  burned  in  the  air.  This  indicates  that  the  former 
is  hydrogen  gas  and  the  latter  oxygen  gas. 

Since  pure  water  is  an  almost  perfect  non-conductor  of  elec- 


PHYSIOLOGICAL    EFFECT. 


195 


Fig.  135. 


tricity  (page  203),  the  probable  explanation  of  this  action  is 
very  closely  like  that  already  given  (page  185) 
for  the  action  in  the  simple  cell.  The  sulphuric 
acid  is  decomposed  ;  H2SO4  becomes  H2  +  SO4 ; 
then  SO4  -f  H2O  becomes  H2SO4  +  O.  It  is  cer- 
tain that  water  is  ultimately  decomposed,  for  no 
sulphuric  acid  is  lost.  This  electrolysis  shows 
that  water  is  composed  of  two  parts  by  volume 
of  hydrogen  to  one  part  of  oxygen.  (Why 
ought  not  copper  poles  to  be  used  in  this  experi- 
ment? Ascertain,  by  inserting  a  galvanometer 
in  the  circuit,  whether  the  current  is  weakened  s--,- 


by  performing  the  work  of  electrolysis.) 

When  the  poles  of  a  strong  battery  are  applied 
for  some  time  to  a  person's  skin,  blisters  appear  under  the  poles. 
The  serous  fluid  that  comes  from  the  vesicles  under  the  positive 
pole  is  acid  ;  the  fluid  in  the  vesicles  under  the  negative  pole  is 
alkaline. 

§  170.     Physiological  effect. —  Experiment.     Place  the  tip 

of  the  tongae   between  the  two  poles  of  ;i  single  cell,  so  that  the 
tongue  may  form  part  of  the  circuit; 
a  stinging  sensation  is  felt,  accom- 
panied by  a  peculiar  acrid  taste. 


Fig.  136. 


When  a  battery  is  known  not 
to  be  very  powerful,  the  tongu  j 
serves  as  a  very  convenient  gal- 
vanoscope,  to  determine  whether 
the  circuit  is  in  working  condition, 
and  approximately  the  strength  of 
the  current.  If  the  crural  nerve 
(a  white  cord  next  the  backbone) 
of  a  frog,  recently  killed,  is  laid 
bare,  and  one  of  the  poles  of  a  battery  is  applied  to  it,  on  touch- 
ing a  naked  muscle  of  a  leg  with  the  other  pole,  the  muscles  are 
instantly  convulsed  and  the  leg  drawn  up,  as  represented  by  the 


196  ELECTRICITY   AND    MAGNETISM. 

dotted  lines  in  Figure  136.  The  same  convulsion  occurs  at  the 
instant  the  circuit  is  broken.  B}~  touching  the  nerve  with  a 
piece  of  zinc,  and  the  muscle  with  a  copper  wire,  as  represented 
in  Figure  136,  similar  convulsions  occur,  on  bringing  the  free 
ends  of  the  metals  in  contact,  and  on  their  separation.  The 
cause  is  obvious ;  for  the  two  metals  and  the  moisture  of  the 
flesh  furnish  all  the  essentials  of  a  voltaic  element. 

The  irritability  of  nerves  and  muscles  begins  to  diminish  after 
death,  and  sooner  or  later  disappears.  It  disappears  much 
sooner  in  warm  than  in  cold-blooded  animals.  In  the  limb  of 
a  frog  that  is  properly  protected,  and  kept  at  a  cool  temperature, 
it  may  remain  for  two,  three,  or  even  four  weeks.  If  one  pole 
is  armed  with  a  soft  sponge,  wet  with  salt  water,  and  pressed 
firmly  on  the  closed  eyelid,  while  the  other  is  applied  at  the 
back  of  the  neck,  or  held  in  the  hand,  making  and  breaking  the 
circuit  will  cause  a  sensation  of  light  of  various  colors. 

§  171.  Magnetic  effect.  —  Experiment.  Obtain  an  insulated l 
copper  wire,  wind  twenty  or  more  turns  around  a  rod  of  well-annealed 
iron,  10cm  long  and  about  lcm  in  diameter,  and  close 
the  circuit.  Bring  a  nail  (Fig.  137),  or  other  piece 
of  iron,  near  the  rod.  The  rod  attracts  the  nail 
with  much  force,  and  this  nail  will  attract  other 
nails.  The  rod  has  acquired  all  the  properties  of  a 
magnet,  as  will  be  seen  hereafter.  But  the  instant 
the  circuit  is  broken,  the  iron  loses  its  magnetic 
force,  and  the  nails  drop. 

The  more  times  the  wire  is  wound  around 
the  rod,  within  a  certain  limit,  the  more  power- 
fully is  it  magnetized.  This  arrangement  is 
called  an  electro-magnet,  because  it  is  a  mag- 
net produced  by  electricity-  The  rod  of  iron 
is  called  its  core,  and  the  coil  of  wire  the  helix. 

1  Insulated,  covered  with  cotton  or  silk,  to  prevent  electricity  from  passing  from 
one  eection  of  wire  to  another  in  contact  with  it,  without  passing  through  .he  whole 
length  of  the  wire. 


STRENGTH    OF   CURRENT.  197 

In  order  to  take  advantage  of  the  attraction  of  both  ends  or 
poles  of  the  magnet,  the  rod  is  most  frequently  bent  in  a  U-shape 
(A,  Fig.  138),  and  then  it  is  Fig.  138. 

called  a  horse-shoe  magnet. 
Sometimes  two  iron  rods  are 
used,  connected  by  a  rectan- 
gular piece  of  iron,  as  a,  in 
B  of  Figure  138.  The  method 
of  winding  is  such  that  if  the  iron  core  of  the  horse-shoe  were 
straightened,  or  the  two  spools  were  placed  together,  end  to 
end,  one  would  appear  as  a  continuation  of  the  other.  A 
piece  of  soft  iron,  6,  placed  across  the  ends,  and  attracted  by 
them,  is  called  an  armature.  The  piece  of  iron  a  is  called  a 
back  armature. 

XXX.     ELECTRICAL    MEASUREMENTS. 

The  wonderful  developments  of  electrical  science  in  recent 
years  are  almost  wholly  due  to  a  better  understanding  of  what 
electrical  measurements  can  and  ought  to  be  made,  and  how  to 
make  them.  Most  of  this  increased  knowledge  has  been  gained 
since  the  first  Atlantic  cable  failed  in  1858.  Let  us  learn  how 
to  make  some  of  them. 

§  172.  Strength  of  current.  —  It  is  evident  that  the  ther- 
mal and  luminous  effects  of  electrical  discharges,  electro-chemi- 
cal decomposition,  the  deflection  of  the  magnetic  needle,  the 
magnetization  of  iron,  and  even  physiological  effects,  or  any 
external  manifestation,  may  be  employed  to  detect  the  presence 
of  an  electric  current,  in  a  circuit  however  extended.  It  is  also 
obvious  that  the  magnitude  of  these  effects  may  serve  to  measure 
the  strength  of  the  current.  Now,  as  the  quantity  of  water  that 
passes  through  a  given  pipe  in  a  minute  or  an  hour  indicates 
the  strength  of  the  current,  so  by  the  strength  of  an  electric  cur- 
rent is  meant  the  quantity  of  electricity  that  passes  through  an 
electrical  conductor  in  a  unit  of  time. 


198 


ELECTRICITY    AND   MAGNETISM. 


§  173.  Voltameter.  —  The  quantity  of  electricity  that  passes 
any  cross  section  of  any  conductor  in  the  same  circuit,  however 
long,  is,  unless  there  is  a  leakage  at  some  point,  necessarily  the 
same.  We  may,  therefore,  introduce  a  platinum  wire  into  any 
part  of  the  circuit,  and  measure  the  strength  of  a  current  by  the 
temperature  to  which  the  wire  is  raised ;  or  we  ma}-  decompose 
water  and  collect  the  gases  resulting  therefrom  ;  the  strength  oj 
current  is  measured  by  the  quantity  of  gas  liberated  in  a  unit 
of  time.  The  latter  arrangement,  called  a  voltameter,  is  easily 
rig.  139.  constructed  sufficiently  accurate  for  many  pur- 

poses, and  should  be  constructed  and  used  by 
la.  every  pupil. 

In  Figure  139,  a  is  a  glass  tube  50cm  long  and  3cm  iu 
diameter  (a  much  shorter  tube  will  answer;  for  ex- 
ample, a  large  sized  test-tube),  closed  at  one  end, 
and  graduated  in  cubic  centimeters  (this  may  be 
clone  by  means  of  a  paper  scale  pasted  on  one  side 
of  the  tube)  ;  b  is  a  bottomless  glass  bottle  of  about 
1  liter  capacity.  Through  the  stopper  of  the  bottle 
pass  two  insulated  wires,  terminating  in  platinum 
strips,  which  are  introduced  a  little  way  into  the 
tube.  The  tube  is  filled  with  water  slightly  acidu- 
lated with  sulphuric  acid,  and  its  orifice  is  im- 
mersed in  the  same  kind  of  liquid,  which  partly  fills 
the  bottle.  When  the  wires  are  connected  with  a 
battery  of  two  or  more  cells  in  series  (see  page  208) , 

the  gas  arising  from  the  decomposition  of  the  water  will  collect  in 

the  top  of  the  tube  and  displace  the  liquid. 

§  174.  Galvanometer.  —  The  instrument  in  most  common 
use  for  measuring  current  strength  is  the  magnetic  needle,  which, 
besides  its  ordinary  use  as  a  galvanoscope,  performs  the  still 
more  important  office  of  a  galvanometer.  The  simple  magnetic 
needle,  used  as  already  described,  answers  tolerabty  well  when 
the  currents  are  strong,  but  it  is  not  sensitive  enough  to  be 
sensibly  moved  by  very  weak  currents.  If  two  equal  currents, 
flowing  in  the  same  direction,  are  placed  one  above  and  the 


TANGENT   GALVANOMETER.  199 

other  below  a  magnetic  needle,  they  tend  to  produce  opposite  de- 
flections, and  to  neutralize  one  another's  effect,  so  that  no  deflec- 
tion occurs.  Evidently,  if  they  flow  in  opposite  directions,  they 
tend  to  produce  a  deflection  in  the  same  direction,  and  the  result 
is  a  deflection  twice  as  great  as  that  produced  by  a  single  cur- 
rent. The  same  result  is  accomplished  if  the  same  current  is 
made  to  pass  both  above  and  below  a  needle,  as  in  A,  Figure 
140.  If  the  wire  were  carried  four  times  around  the  needle,  as 

Fig.  140. 


in  B,  the  influence  of  the  current  on  the  needle  would  be  about 
four  times  that  of  a  single  turn.  Very  sensitive  galvanometers, 
constructed  on  this  principle,  often  with  thousands  of  turns 
of  wire,  are  sometimes  called  long-coil  galvanometers,  in  dis- 
tinction from  those  having  few  turns,  which  are  called  short-coil 
galvanometers. 

§  175.  Tangent  galvanometer.  —  The  arrangement  de- 
scribed above  is  more  commonly  used  as  a  galvanoscope  than  a 
galvanometer,  though  it  ma}T  be  so  calibrated  as  to  answer  the 
latter  purpose.  The  law  connecting  the  current  strength  with 
the  deflection  of  the  needle  of  this  galvanometer  is  not  known ; 
but  in  another  form,  called  the  tangent  galvanometer,  the  rela- 
tion is  expressed  in  a  simple  tangent  of  the  angle  of  deflection. 
This  apparatus  is  constructed  on  the  principle  that  the  strength 
of  currents  are  proportional  to  the  tangents  of  the  angles  of 
deflection,  when  the  needle  is  very  short  in  comparison  with  the 
diameter  of  a  circle  described  by  a  current  circulating  around 
it. 


200 


ELECTRICITY    AND   MAGNETISM. 


A  magnetic  needle,  about  2.5cm  long,  is  suspended  freely  by  an  un- 
twisted thread  n,  Figure  141,  in  the  center  of  a  copper  hoop  a,  about 
30cm  in  diameter,  which  terminates  in  the  wires  ww' ;  and  these  are  con- 
nected with  the  battery  whose  current  is  to  be  measured.  A  circular 
card-board  cc,  containing  a  circle  divided  to  degrees  to  indicate  the 
extent  of  deflection,  is  placed  beneath  the  needle.  The  ring  being 
placed  so  that  it  is  parallel  with  the  needle,  the  needle  points  to  0°  on 
the  scale.  When  a  current  passes  through  the  ring  a,  the  needle  is 
deflected.  The  tangents  of  the  angles  of  deflection  may  be  found  by 

Fig.  141. 


reference  to  a  Table  of  Natural  Tangents  in  Section  D  of  the  Appendix, 
and  the  relative  strengths  of  currents  may  be  determined  by  the  law 
given  above.  The  construction  of  a  very  simple  galvanometer  that 
may  be  used  as  a  tangent  galvanometer,  and  which  will  answer  all 
requirements  of  this  book,  may  be  found  in  Section  E  of  the  Appendix. 

§  176.  Experiments  in  measurements.  —  Inasmuch  as 
the  magnitude  of  the  effects  that  can  be  produced  by  an  elec- 
tric current,  or  the  amount  of  work  that  can  be  done  by  it, 
depends  upon  the  strength  of  the  current,  it  is  of  the  utmost 
importance  to  understand  the  principles  by  which  it  is  regu- 
lated. A  few  experiments  will  make  this  apparent.  Provide 
four  coils  or  spools  of  insulated  wire.  Mark  the  coils  A,  B,  C, 
and  D.  Let  A  contain  100  ft.  (about  1  Ib.)  of  No.  16  copper 


ON  WHAT  STRENGTH  OF  CURRENT  DEPENDS.   201 

wire ;  B  and  C  respectively  100  ft.  and  50  ft.  of  No.  30  copper 
wire  ;  and  D  50  ft.  of  No.  30  German  silver  wire. 

Experiment  1.  Place  a  galvanometer  G  and  coil  A  in  the  same 
voltaic  circuit,  connected  as  shown  in  Figure  142.  Note  the  number 
of  degrees  the  needle  is  deflected.  Next  substitute  coil  B  for  A,  and 
note  the  deflection.  The  deflection  is  less  than  before,  showing  that 
of  two  wires  of  the  same  material  and  equal  length,  the  larger  transmits, 
from  the  same  source,  the  stronger  current. 

Fig.  142. 


Experiment  2.  Place  coil  C  in  the  circuit  with  B,  and  compare  the 
deflection  with  that  produced  when  B  alone  was  in  the  circuit.  The 
deflection  is  less  than  before.  (Why?)  Take  B  out,  and  leave  C  in 
the  circuit.  The  deflection  is  greater  than  when  B  alone  was  in  the 
circuit.  Other  things  being  the  same,  the  shorter  wire  transmits,  from 
the  same  source,  the  stronger  current. 

Experiment  3.  Introduce  D  in  the  place  of  C,  and  compare  the 
strengths  of  the  currents  in  these  two  wires.  The  copper  wire  trans- 
mits, from  the  same  source,  a  stronger  current  than  the  German  silver  wire 
of  the  same  length  and  size. 

Experiment  4.  Compare  the  currents  furnished  by  a  Grove  or 
Bunsen,  and  a  Smee  or  a  gravity  cell,  when  the  same  coil,  for  in- 
stance B,  is  in  the  circuit.  The  Grove  or  Bunsen  cell  gives  the  stronger 
current. 

§  177.  On  what  strength  of  current  depends.  —  It  ap- 
pears that  the  strength  of  the  current  varies  not  onl}-  with  the 


202  ELECTRICITY  AND   MAGNETISM. 

size,  length,  and  kind  of  conductor,  but  also  with  the  kind  of 
battery  used.  These  will  be  considered  consecutively.  It  is 
evident  that  all  conductors  do  not  allow  the  current  to  pass  with 
equal  facility ;  in  other  words,  some  conductors  offer  more  re- 
sistance to  the  passage  of  a  current  than  others.  The  larger 
conductor  offers  less  resistance  than  the  smaller.  It  is  found 
by  experiment  that  (1)  the  strength  of  currents  varies  directly 
as  the  areas  of  the  cross  sections  of  the  conductors,  or  the  squares 
of  the  diameters  of  cylindrical  conductors,  inasmuch  as  areas 
vary  as  the  squares  of  their  diameters.  (2)  It  varies  in- 
versely as  the  length  of  the  conductor,  i.e.,  if  a  wire  one  mile 
long  offers  a  certain  amount  of  resistance,  a  wire  two  miles 
long  will  offer  twice  as  much  resistance.  (3)  It  varies  in- 
versely as  the  specific  resistances  of  the  substances  used  for  con- 
ductors. The  conducting  power  of  a  substance  is  the  reciprocal 
of  its  resistance.  Hence,  if  we  know  the  conducting  power  of 

an\'  wire,  we  know  that  the  resistance  = : •  ;  or  the 

1  conductivit}^ 

conductivity  = • 

resistance 

Resistance  is  expressed  in  units  called  ohms1  (see  §  181). 
The  student  can  easily  provide  himself  with  a  standard  having 
approximately  a  resistance  of  one  ohm,  by  obtaining  40  feet  of 
No.  24  ordinary  copper  wire  0.5mm  in  diameter. 

§  178.  Formula  for  resistance.  —  Having  found  that  re- 
sistance varies  directly  as  the  length,  and  inversely  as  the  squares 
of  the  diameters  of  conductors,  we  may  include  all  its  laws  in  the 
formula  ^  ^  I 

R=K5; 

in  which  R  =  the  resistance,  Z  =  the  length,  and  d  the  diameter 
of  a  cylindrical  conductor.  K  is  a  constant,  such  that  when  the 
material  of  the  wire  is  known  and  the  denomination  in  which 
I  and  d  are  expressed,  a  value  of  K  taken  from  a  table  may  be 

1  Ohm,  from  the  name  of  a  German  savant,  Dr.  G.  S.  Ohm,  who  first  enunciated 
the  laws  which  determine  the  strength  of  currents. 


FORMULA   FOR   INTERNAL   RESISTANCE.  203 

substituted  in  the  equation,  and  thus  enable  us  to  find  the  value 
of  R  in  ohms.  Thus  let  it  be  required  to  find  R  of  1000  ft.  of 
copper  wire  0.1  inch  in  diameter.  The  table  gives  the  value  of 
K  as  9.72  when  the  length  of  the  wire  is  measured  in  feet,  and 
its  diameter  in  thousandths  of  an  inch  ;  since  0.1  inch  equals  100 

thousandths,  R  =  9.72  x  ^      =  Q.972  ohm. 


In  the  following  table  are  given  the  relative  resistances  of 
several  substances,  and  the  values  of  K  in  the  above  equation 
when  I  is  expressed  in  feet  and  d  in  thousandths  of  an  inch. 

REFERENCE  TABLE  OF  RELATIVE   RESISTANCES,  ETC. 

Rel.  Resist.  K. 

Silver  ..................  @0°C  ..................  1.00  .....  9.15 

Copper  .................      "        .................  1.06  .....  9.72 

Zinc  ....................      "        .................  3.74  .....  34.2 

Platinum  ...............      "        .................  6.02  .....  55.1 

Iron  ....................      "        ..........  .......  6.46  .....  59.1 

German  silver  ...........      "        ...............  .  .  13.91  .....  127.3 

Mercury  ................      "        .................  63.24  .....  578.6 

Rel.  Resist. 

Nitric  acid  —  commercial.  ...  @  15  to  28  C  .....................  1,100,000 

Sulphuric  acid,  1  to  12  parts  water   "    ......................  2,000,000 

Common  salt  —  saturated  sol.  "    .......................  3,200,000 

Sulphate  copper  "  "    ...............  .  ......  18,000,000 

Distilled  water  ...........................  not  less  than  10,000,000,000 

Glass  ......................  @  200°  C.  ..............  15,000,000,000,000 

Gutta  percha  ...............  @     0°  C.  .  .  .5,000,000,000,000,000,000,000 

The  resistance  of  metals  increases  slowly  as  the  temperature 
rises  ;  but  that  of  liquids  and  the  other  poor  conductors  in  the 
second  list  decreases  very  rapidly  with  a  rise  in  temperature. 
The  resistance  of  ordinary  impure  metals  is  often  much  higher 
than  that  given  in  the  table. 

§  179.  Formula  for  internal  resistance.  —  Resistance  in 
a  voltaic  circuit  may  be  divided,  for  convenience,  into  two  parts  ; 
viz.,  internal  resistance  (r),  which  the  current  encounters  in 


204  ELECTRICITY  AND   MAGNETISM. 

passing  through  the  liquid  between  the  two  plates  in  the  cell, 
and   external  resistance    (R),  which  it  Suffers  in  the  remain- 
der of  its  path.     The  internal  resistance  is  governed  by  the 
same  laws  as  the  external  resistance.     In  this  case 
r  _  yr     distance  of  the  plates  apart  (I) 
areas  of  the  plates  submerged  (d2) 

QUESTIONS   AND    PROBLEMS. 

1.  What  length  of  copper  wire  will  have  the  same  resistance  as  a 
mile  of  iron  wire  of  the  same  diameter? 

2.  How  can  you  reduce  the  resistance  of  an  iron  wire  to  that  of  a 
copper  wire  of  the  same  length? 

3.  About  how  much  is  the  conductivity  of  water  affected  by  adding  a 
little  sulphuric  acid? 

4.  How  many  times  greater  is  the  resistance  of  dilute  sulphuric  acid 
than  that  of  copper? 

5.  Upon  what  does  the  resistance  offered  by  the  liquid  part  of  a 
circuit  depend,  and  how  may  it  be  diminished  ? 

6.  What  is  the  resistance  of  500  ft.  of  copper  wire  .014  inch  in 
diameter  (No.  30  B.W.  gauge)?    Arts.  24.7  +  ohms. 

7.  What  length  of  copper  wire  .006  inch  in  diameter  (No.  38)  will 
offer  a  resistance  of  1  ohm  ? 

8.  What  is  the  resistance  of  16  yards  of  German  silver  wire  (No.  30) 
.014  inch  in  diameter  ? 

9.  What  is  the  resistance  of  1  mile  of  iron  telegraph  wire,  the  usual 
size  being  .175  inch  in  diameter  ? 

10.   Express  in  ohms  the  resistance  of  1  mile  of  copper  wire,  0.06 


inch  in  diameter?    Ans.  9.72  x  >       =  14.256  ohms. 

uU 

§  180.  Electro-motive  force.  —  The  experiments  described 
in  §  151  show  that  electricity  constantly  flows  in  a  closed  circuit 
containing  a  voltaic  cell  ;  hence  the  cell  has  the  power  of  setting 
electricity  in  motion,  or  an  electro-motive  force  (usually  abbre- 
viated E.M.F.).  Again,  Exp.  4,  §  176,  proves  that  a  Grove 
cell,  in  a  circuit  of  a  given  resistance,  sets  in  motion  a  greater 
quantity  of  electricity  than  a  Smee  or  gravity  cell  ;  hence  we  say 
that  the  E.M.F.  of  a  Grove  cell  is  greater  than  that  of  the  other 
two  kinds  mentioned.  It  has  been  found  that  E.M.F.  depends 


OHM'S  LAW.  205 

solely  upon  the  nature  and  condition  of  the  substances  which  form 
the  battery,  and  is,  consequently,  quite  independent  of  the  size  of 
the  plates  and  their  distance  apart.  The  unit  employed  in  the 
measurement  of  E.M.F.  is  called  a  volt.1  It  is  about  the  E.M.F. 
of  a  current  generated  by  one  gravity  cell.  The  following 
table  exhibits  the  electro-motive  force  in  volts  of  different 
cells  :  — 

TABLE  OF  ELECTRO-MOTIVE  FORCES. 

Gravity  or  Daniell  ......  .  .....  ,:,  ........  0.98  to  1.08  volts. 

Bunsen  and  Grove  ......................  1.76  to  1.95      " 

Leclanche,  at  first  ......................   1.48  to  1.60      " 

Grenet  "        ......................  1.80  to  2.3       " 

Smee  ...................................  65       ____      " 

The  E.M.F.  of  the  last  three  decreases  considerably  if  the  circuit  Is 
closed  for  a  few  minutes.  These  numbers  signify,  for  instance,  that  it 
will  require  195  Smee  cells  to  give  the  same  current  in  a  circuit  (of 
high  resistance)  as  would  be  given  by  65  Grove  cells. 

§  181.  Ohm's  Law.  —  The  law  which  expresses  the  strength 
of  the  current,  and  is  the  basis  of  most  mathematical  calculations 
on  currents,  is  expressed  in  the  formula  known  as  Ohm's  Law. 
Calling  the  current  C,  the  E.M.F.  simply  E,  and  the  whole 
resistance  in  the  circuit  R,  the  formula  expressing  the  law  is 


In  words,  this  means  that  the  strength  of  the  current  is  equal  to 
'he  electro-motive  force  of  the  battery,  divided  by  the  resistance  of 
the  circuit;  i.e.,  C  will  be  greater  or  less  as  E  is  greater  or  less, 
but  will  be  less  when  R  is  greater,  and  greater  when  R  is  less. 

F 

The  above  relation  —  ,  when  the  external  resistance  is  considered 
R 

separately  from  the  internal,  must  be  converted  thus  :  calling 
the  former  R,  and  the  latter  r,  the  expression  becomes 

C-      E 

-ITjT 

1  Volt,  from  the  name  Volta. 


206  ELECTRICITY   AND   MAGNETISM. 

For  single  cells  in  ordinary  use  the  value  of  r  will  usually  be 
between  .5  and  2  ohms. 

The  unit  of  current  strength,  called  an  ampere,  is  the  current 
flowing  in  a  conductor  having  a  resistance  of  1  ohm,  between  the 
ends  of  which  a  difference  of  potential  of  1  volt  is  maintained  ; 
or  it  is  a  current  of  1  coulomb  per  second.  A  coulomb  is  the 
amount  of  electricity  conveyed  in  1  second  by  a  current  of 

1  ampere. 

If  a  cell  has  E  =  1  volt,  and  r  =  1  ohm,  and  the  connecting 
wire  is  short  and  stout,  so  that  R  may  be  disregarded,  then  the 
current  has  a  value  of  1  ampere.  But  if  the  connecting  wire 
has  a  resistance  R,  equal  to  1  ohm,  then 

C  =  —  =  —  =  i  =  .5  ampere. 
R+r      1+1      2 

§  182.  Summary  of  electrical  measurements.  — Just  as 
we  express  an  amount  of  money  in  the  denomination  dollars,  or 
a  mass  of  coal  in  the  denomination  pounds,  we  express  electrical 

Potential,  P  (commonly,  difference  of  P). . .  .in  volts. 

Electro-motive  force,  E "  volts. 

Resistance,  R "  ohms. 

Strength  of  current,  C "  amperes. 

Quantity  of  electricity "  coulombs. 

The  following  will  give  some  idea  of  the  magnitude  of  the 
denominations.  A  gravity  cell  produces  a  difference  of  poten- 
tial or  an  electro-motive  force  (for  these  are  only  different  ways 
of  viewing  the  same  quantity)  of  nearly  1  volt.  To  produce  a 
spark  lmm  long  requires  from  3,000  to  4,000  volts.  A  No.  16 
ordinary  copper  wire  250  ft.  "long  (diameter  .051  inch,  weight 

2  Ibs.)   has  a  resistance  of  about  1  ohm.     About  150  ft.   of 
copper  wire  lmm  in  diameter  has  a  resistance  of  1  ohm.     An 
ordinary  Grove  cell  may  have  an  internal  resistance  of  ^  ohm  ; 
this  cell  will  send  through  125  ft.  of  No.  16  copper  wire  a  cur- 
rent whose  strength  is  1  ampere. 


ARRANGEMENT   OF   BATTERIES.  207 

PROBLEMS. 

1.  What  current  will  be  obtained  from  a  gravity  cell  when  E  =  1 , 
r  —  2  ohms,  and  R  =  10  ohms? 

2.  What  current  may  be  got  from  a  gravity  cell  whose  internal  re- 
sistance is  3  ohms,  and  external  resistance  is  3  ohms  ? 

3.  What  current  will  a  Grove  cell  furnish,  having  the  same  internal 
and  external  resistances  as  the  last? 

§  183.  Arrangement  of  batteries.  —  The  internal  resist- 
ance may  be  diminished  by  placing  the  plates  as  near  to  each 
other  as  practicable,  and  by  employing  large  plates,  and  thereby 
increasing  the  size  of  the  liquid  conductor.  But  it  is  not  always 
convenient  to  emplo}^  very  large  plates,  or  we  may  have  occasion 
to  employ  a  battery  for  certain  purposes,  as  we  shall  see  pres- 
ently, in  which  large  cells  would  be  of  little  or  no  advantage. 
The  same  result  that  can  be  produced  by  a  single  pair  of  large 
plates,  may  be  obtained  by  connecting  the  similar  pi  143 
plates  of  several  pairs  in  separate  cells,  thereby 
practically  reducing  several  pairs  to  one  pair 
having  an  area  equal  to  the  sum  of  the  areas  of 
the  several  pairs.  Figure  143  illustrates  a  method 
of  connecting  cells  for  the  purpose  of  reducing 
the  internal  resistance.  This  is  called  arranging 
cells  parallel,  in  multiple  arc,  or  abreast. 

This  arrangement  is  very  effectual  in  increasing 
the  current-strength  when  the  internal  resistance 
is  the  principal  one  to  be  overcome.  For  instance, 
call  the  electro-motive  force  (E)  of  a  single  cell 
I  volt,  its  internal  resistance  5  ohms,  and  let  the 
plates  be  connected  by  a  short,  thick  wire,  whose 
resistance  may  be  regarded  as  nothing;  then 

"P  1 
C  =  —  =  -=.2  ampere.  Now  connect  10  similar 

r  5 
cells  abreast.  The  size  of  the  liquid  conductor 

being  increased  tenfold,  the   internal  resistance    is   one-tenth 

TT 
as  large,  and  we  have  C  =  -  =  l-s-T51J-  =  2  amperes.  So  that, 


208  ELECTRICITY  AND   MAGNETISM. 

when  there  is  no  external  resistance,  the  current  increases  as 
the  size  of  the  plates  is  increased.  The  same  is  approximately 
true  in  case  the  external  resistance  is  very  small  in  comparison 
with  the  internal  resistance. 

Again,  let  E  =  1,  r  =  5  ohms,  as  above,  but  the  external  re- 
sistance R  =  200  ohms  ;  then  C  = =  .0048+  ampere.  If 

o  -j-  200 

10  pairs  are  connected   abreast,  C  = =  .0049+  ampere. 

i  +  200 

In  this  case,  the  current  is  scarcely  affected  by  increasing  the 
number  of  cells  abreast.  The  question  then  arises,  what  can  be 
done  to  increase  the  current  when  the  external  resistance  is 
necessarily  large ;  as,  for  instance,  when  a  long  telegraph  wire 
is  used.  In  this  case  R,  in  Ohm's  formula,  is  unalterable,  and 
Fjg  144  lessening  r  has  little  effect ; 

so  there  remains  only  one 
way,  viz.,  to  increase  E,  the 
electro-motive  force.  How 
may  this  be  done?  If  the 
current  from  a  cell,  instead 
of  passing  immediate^  out  of 
the  cell  on  its  journey,  is  made 
to  pass  through  another  cell 
first,  one  might  naturally  expect  that  either  the  two  cells  would 
counteract  one  another  in  the  circuit,  or  that  they  would  double 
the  E.M.F.  Experiment  shows  that  the  latter  result  is  the  true 
one,  and  that  the  E.M.F.  is  exactly  proportional  to  the  number 
of  cells  connected  in  series.  Cells  so  connected  as  to  increase 
the  electro-motive  force  are  said  to  be  joined  in  series  or  tandem. 
The  method  of  connecting  the  cells  for  this  purpose  is  shown  in 
Figure  144. 

It  will  be  seen  that  in  the  multiple  arc  (Fig.  143)  all  the  zinc 
plates  are  connected  with  one  another,  and  all  the  copper  plates 
with  one  another.  In  the  tandem  arrangement  the  zinc  of  one 
cell  is  connected  with  the  copper  of  the  next  throughout. 


I  <l  [ 


ARRANGEMENT   OF   BATTERIES. 


209 


In  the  last  example  given  above,  let  us  see  what  would  be  the 
effect  of  connecting  the  10  cells  in  series.  In  this  case  E  is 
increased  tenfold ;  and,  as  the  current  is  Fig.  145. 

obliged  to  pass  through  the  liquid  of  10 
cells  instead  of  one,  the  internal  resistance 
will  also  be  increased  tenfold ;  hence, 

C  =  _ll  XJ^ =  .0400  ampere,  more 

(5x  10) +  200 

than  eight  times  as  much  as  before.  Thus 
it  appears  that,  ivhen  the  external  resistance 
is  large  in  comparison  with  the  internal 
resistance,  the  current  may  be  largely  in- 
creased by  multiplying  the  cells  in  series; 
in  other  words,  by  forming  a  battery  of 
great  electro-motive  force.  In  long  tele- 
graph lines  the  battery  is  made  up  of  hun- 
Fig.i46.  dreds  of 

cells   joined 
in  series. 

Large  cells  are  used  simply  be- 
cause the  fluids  last  longer,  and 
so  the  cells  need  less  attention. 

Sometimes  a  combination  of  the 
two  arrangements  gives  a  stronger 
current  than  either  alone.  The 
cells  may  be  grouped  together  in 
pairs  (as  in  Figure  145),  or  in 
triplets  (as  in  Figure  146) ,  so  as 
to  increase  the  electro-motive 
force ;  then  the  several  groups 
may  be  connected  abreast,  to  reduce  the  internal  resistance. 


'•••-    .    •'  -        o~\ 

I  II 

x^lrv      /-iOO-x 

I  ft  -1-1 


PROBLEMS. 

1.  Suppose  that  the  cells  in  the  last  example  above  be  so  increased 
in  size  that  r  in  each  =  .5  ohm,  what  current  will  be  got  from  the 
battery? 


210  ELECTRICITY   AND   MAGNETISM. 

2.  What  current  is  there  on  a  telegraph  wire  100  miles  long,  wheu 
it  is  in  circuit  with  40  Grove  cells,  the  internal  resistance  of  each  cell 
being  .5  ohm,  the  icsistance  of  the  wire  15  ohms  to  the  mile,  and  the 
resistance  of  the  earth  connections  100  ohms? 

3.  An  electric  bell,  whose  resistance  is  .5  ohm,  is  found  to  require  a 
current  of  .02  ampere  to  ring  it.     How  many  gravity  cells  will  it  require, 
if  the  circuit  consists  of  an  iron  wire  1  mile  long,  having  a  diameter 
of  .165  iu.  (^  4.29"""),  disregarding  the  resistance  of  the  cells  ? 

4.  Which  is  the  better  arrangement  (i.e.,  abreast  or  tandem)  of  210 
"gravity  cells,  each  of  3  ohms  resistance,  against  an  external  resistance 

of  10  ohms,  and  what  will  be  the  current  with  each? 

5.  In  a  battery  of  10  cells  connected  in  series,  ten  times  as  much 
zinc  and  acid  are  consumed  as  in  1  cell.      Show  how  about  nine- 
tenths  of  the  chemicals  may  be  wasted. 

6.  In  a  certain  circuit  a  battery  of  40  gravity  cells,  each  of  3  ohms 
resistance,   is  used.     The  cells  are  arranged  in  two  groups  of  20  cells 
each  in  series,  and  the  two  groups  are  so  connected  as  to  diminish 
the  internal  resistance.    If  It  =  120  ohms,  what  current  will  be  obtained? 

7.  Devise  various  arrangements  of  30  cells  in  which  r=.S  ohm. 
Which  arrangement  is  best  when  R=  10  ohms?  when  R=  30  ohms? 

V    . 

§  184.  General  conclusions.  —  A  perfect  battery  would 
have  the  following  qualities  :  — 

1.  It  would  have  a  high  electro-motive  force. 

2 .  Its  E.M.F.  would  be  constant,  whether  used  to  produce  strong 
or  weak  currents. 

3.  It  would  have  a  small  and  constant  interned  resistance. 

No  battery  fulfils  perfectly  all  these  conditions  ;  so,  in  practice, 
the  use  to  which  the  battery  is  to  be  put,  its  first  cost,  and  the 
trouble  and  expense  of  keeping  it  in  order,  determine  which 
of  these  qualities  shall  be  given  up.  The  question,  What  is  the 
best  battery?  is  discussed  in  the  Appendix,  Section  F. 

A  current  from  a  single  cell,  traversing  a  short,  thick  wire, 
will  produce  as  large  a  deflection  of  a  magnetic  needle  as  a  cur- 
rent from  500  cells  connected  in  series.  On  the  other  hand,  a 
message  has  been  transmitted  through  the  Atlantic  cable,  whose 
resistance  is  about  7,000  ohms,  by  a  current  generated  in  a 


GENERAL    CONCLUSIONS. 

lady's  thimble,  and  the  signals  produced  were  as  distinct  as 
those  that  would  be  produced  by  a  cell  of  several  square  feet. 
In  this  case,  the  quantity  of  electricity  that  passed  depended 
chiefly  upon  the  E.M.F.  of  the  battery,  and  not  upon  its  inter- 
nal resistance.  (How,  in  the  former  case,  can  the  current  be 
increased?  How  could  it  have  been  increased  in  the  latter 
case  ?) 

The  same  strength  of  current  that  would  fuse  an  inch  of 
platinum  wire  would  fuse  a  mile  of  the  same  wire.  But  while 
one  cell  would  fuse  the  inch  of  wire,  it  would  require  the  E.M.F. 
of  many  hundred  to  maintain  the  same  strength  of  current  in 
the  mile  of  wire. 

A  battery  of  three  cells  arranged  abreast  will  fuse  a  certain 
length  of  platinum  wire,  but  will  not  be  felt  by  a  person  holding 
the  poles  in  his  hands  ;  while  a  battery  of  100  cells  in  series  will 
not  fuse  the  same  wire,  but  will  produce  quite  a  shock. 

The  power  of  an  electro-magnet  depends  largely  upon  the 
number  of  times  a  given  current  circulates  around  its  core,  and 
upon  the  nearness  of  the  current  to  the  core ;  for  compactness, 
and  to  keep  the  current  near  the  core,  a  fine  wire  must  then  be 
used.  But  a  long,  thin  wire  would  offer  large  resistance,  that 
might  so  reduce  the  current  as  to  more  than  offset  the  advan- 
tage that  would  otherwise  be  gained.  Hence,  when  there  is 
little  other  resistance  in  a  circuit,  a  large  wire  with  few  turns 
will  give  the  strongest  electro-magnet.  But  if  an  electro-magnet 
is  to  be  used  in  a  circuit  with  other  large  resistance,  then  the 
introduction  of  a  helix  of  many  turns  of  fine  wire  would  add 
little  more  resistance  comparatively,  so  the  strength  of  the  cur- 
rent would  be  reduced  but  little,  while  a  great  gain  would  be 
made  in  the  effect  on  the  core.  For  the  same  reason,  a  galva- 
nometer intended  to  be  used  in  circuits  where  there  is  little 
resistance,  should  contain  only  a  few  turns  of  large  wire ;  but 
if  it  is  to  be  used  with  large  resistance,  it  should  contain  a 
long,  fine  wire.  Electro-magnets  and  galvanometers  should  be 
adapted  to  the  circuits  in  which  they  are  used. 


212  ELECTRICITY   AND   MAGNETISM. 

QUESTIONS. 

1.  A  bell  in  Washington  is  to  be  rung  by  the  action  of  an  electro- 
magnet.    The  current  used  comes  from  a  battery  in  New  York.     How 
should  the  electro-magnet  be  constructed? 

2.  If  you  wished  to  measure  the  current,  by  the  introduction  of  a 
galvanometer  into  the  circuit  in  Washington,  how  should  it  be  made? 

3.  Would  it  require  a  different  galvanometer  if  it  were  to  be  intro- 
duced into  the  same  circuit  in  New  York,  only  a  few  feet  from  the 
battery? 

4.  Provided  there  were  no  leakages,  how  would  the  deflections  at 
the  two  places  compare? 


XXXI.  MAGNETS  AND  MAGNETISM. 

§  185.  Permanent  and  temporary  magnets.  —  One  of  the 
most  familiar  pieces  of  physical  apparatus  is  a  magnet.  We 
know  how  it  can  pick  up  bits  of  iron  and  steel.  By  the  aid  of 
a  small  instrument  already  studied,  we  may  make  a  pair  of  small 
magnets,  and  study  their  actions  and  laws. 

Experiment.  Take  the  electro-magnet,  described  on  page  196,  and 
a  couple  of  sewing  needles  or  larger  steel  rods.  Apply  these  needles, 
one  at  a  time,  to  one  end  of  the  electro-magnet,  and  draw  them  several 
times  across  it  from  end  to  end,  always  in  the  same  direction,  and  not 
rubbing  back  and  forth.  Repeat  the  operation  with  an  iron  wire  of 
the  same  size ;  both  the  wire  and  the  steel  are  attracted  by  the  electro- 
magnet, but  the  iron  wire  more  strongly.  Observe  that  both,  while  in 
contact  with  the  electro-magnet,  possess  the  power  of  attracting  bits 
of  iron ;  but,  on  removing  them,  the  steel  is  found  to  retain  the  property 
it  had,  while  the  iron  does  not. 

Both  of  them  exerted  that  peculiar  force  called  magnetic  force, 
or  possessed  the  property  called  magnetism;  that  is,  both  were 
magnets  ;  but,  as  the  steel  retains  its  power,  it  is  called  a  perma- 
nent magnet  in  distinction  from  a  temporary  magnet,  like  the 
iron  wire  or  the  electro-magnet  itself.  The  quality  of  steel  by 
which  it  at  first  resists  the  power  of  magnets,  and  resists  the 
escape  of  magnetism  which  it  has  once  acquired,  is  called  coer- 


LAW    OF   MAGNETS.  213 

cive  force.  The  harder  steel  is,  the  greater  is  its  coercive  force. 
Hence,  highly  tempered  steel  is  used  for  permanent  magnets. 
Hardened  iron  possesses  some  coercive  force  ;  hence,  the  cores 
of  electro-magnets  should  be  made  of  the  softest  iron,  that  they 
r  acquire  and  part  with  magnetism  instantaneously. 


§  186.    Law  of  magnets.  —  Experiment  1.     Suspend  the  two 
magnets,  each  in  a  horizontal  position,  by  threads  that  will  not  untwist, 
and    several  feet 
distant  from  each 
other.  When  they 

COme  tO   rest,  no- 

Permanent  magnet.  Induced  magnets. 

tice  that  they  have 

taken  up  a  direction  nearly  north  and  south.     Tie  a  thread  on  the  end 

of  each  that  points  to  the  north. 

This  end,  or  pole,  as  it  is  usually  called,  we  will  speak  of  as 
the  N-end,  +,  or  marked  end  or  pole,  while  the  other  is  the 
unmarked,  —  ,  or  S-end  or  pole. 

Experiment  2.  Bring  the  marked  end  of  one  of  the  magnets  near 
to  the  unmarked  end  of  the  other;  they  attract  one  another.  Next 
bring  the  marked  end  of  one  near  to  the  marked  end  of  the  other  ;  they 
repel  one  another.  Bring  the  unmarked  ends  near  one  another  ;  they 
repel  one  another. 

We  discover  the  following  law  of  magnets  :  Like  poles  repel, 
unlike  poles  attract  one  another. 

* 

§  187.  Magnetic  transparency  and  induction.—  Experi- 
ment. Interpose  a  piece  of  glass,  paper,  or  wood-shaving  between 
the  two  magnets.  These  substances  are  not  themselves  perceptibly 
affected  by  the  magnets,  nor  do  they  in  the  least  affect  the  attraction 
or  repulsion  between  the  two  magnets. 

Substances  that  are  not  susceptible  to  magnetism  are,  like 
glass,  paper,  and  wood,  magnetically  transparent.  When  a 
magnet  causes.  another  body,  in  contact  with  it  or  in  its  neigh- 
borhood, to  become  a  magnet,  it  is  said  to  induce  magnetism  in 
that  body,  i.e.,  it  injluences  it  to  be  like  itself.  As  attraction, 


214  ELECTRICITY   AND   MAGNETISM. 

and  never  repulsion,  occurs  between  a  magnet  and  an  unmag- 
netized  piece  of  iron  or  steel,  it  must  be  that  the  magnetism 
induced  in  the  latter  is  such  that  opposite  poles  are  adjacent ; 
that  is,  a  N  or  +pole  induces  a  S  or  —pole  next  itself,  as  shown 
in  Figure  147. 

§  188.   Polarity.  —  Experiment  1.    Strew  iron  filings  on  a  flat 
Fig.  148.  surface,  and  lay  a  bar  magnet  on 

them.  On  raising  the  magnet,  it 
is  found  that  large  tufts  of  filings 
cling  to  the  poles,  as  in  Figure 
148,  especially  to  the  edges ;  but  the  tufts  diminish  regularly  in  size 
from  either  pole  towards  the  center,  where  none  are  found. 

Magnetic  attraction  is  greatest  at  the  poles,  and  diminishes 
towards  the  center,  tvhere  it  is  nothing,  or  the  center  of  the  bar  is 
neutral.  The  dual  character  of  the  magnet,  as  exhibited  in  its 
opposite  extremities,  is  called  polarity,  and  magnetism  is  styled 
a  polar  force.  If  a  magnet  is  broken  at  its  neutral  line,  as  in 
Exp.  1,  p.  28,  it  is  found  that  equal  and  opposite  polarities 
Fig.  149.  exist  where  there  is  ordinarily  no 

evidence  of  them. 


Experiment  2.  Place  a  copper  wire, 
through  which  a  very  strong  current  of 
electricity  is  passing,  in  a  heap  of  iron  filings,  — then  raise  the  wire; 
filings  cling  to  the  wire  somewhat  as  they  do  to  a  magnet,  as  shown  in 
figure  149. 

This  experiment,  and  those  with  the  electro-magnet  and  the 
deflection  of  the  magnetic  needle  by  an  electric  current,  and  a 
multitude  of  others  that  the  pupil  will  meet  with,  cannot  fail  to 
convince  him  that  an  intimate  relation  exists  between  electricity 
and  magnetism,  which,  though  differing  in  many  of  their  prop- 
erties, yet  alike  in  many,  and  almost  invariably  accompany- 
ing one  another,  and  constantly  merging  one  -  into  the  other, 
appear  as  if  they  were  only  different  manifestations  of  one  and 
the  same  agent. 


ATTRACTION   OF   CURRENTS. 


215 


§  189.   Attraction  and  repulsion  between  currents. — 
Let  us  study  still  further  Fi    150  Fio.  151 

the  properties  of  the  cur- 
rent. 


Battery 


Fig.  152. 


Experiment  1.  Suspend 
two  copper  wires  (Fig. 
150),  each  50cm  long,  and 
about  5mm  apart,  with  their 
lower  extremities  dipping 
about  2mm  into  mercury,  so 
as  to  move  with  little  re- 
sistance either  toward  or 
from  each  other.  In  Fig- 
ure 150  the  current  divides 
itself  and  flows  down  both 
wires  to  the  liquid,  so  that 

that  part  of  the  circuit  presents  parallel  currents  flowing  in  the  same 
direction.  Figure  151  is  the  same  apparatus,  with  the  connections  so 
made  that  the  current  flows  down  one  wire  and  up  the  other,  and  we 
have  an  example  of  parallel  currents  flowing  in  opposite  directions.  In 
the  former  case  the  wires  mutually 
attract  one  another.  In  the  latter 
there  is  mutual  repulsion. 

Hence,  the  First  Law  of  Cur- 
rents :  Parallel  currents  in  the  sam^ 
direction  attract  one  another ;  par- 
allel currents  in  opposite  directions 
repel  one  another. 

An  interesting  illustration  of  the 
former  part  of  this  law  can  be  ar- 
ranged as  in  Figure  152.  A  bat- 
tery wire  is  bent  in  the  form  of  a 
spiral  coil.  At  a  the  wire  is  broken , 
mid  one  end  dips  just  below  the  surface  of  mercury  in  a  glass, 
while  the  other  end  is  placed  in  the  same  liquid  at  a  little  dis- 
tance from  the  first.  When  the  circuit  is  closed  the  current  will 
be  parallel  with  itself,  and  will  flow  in  the  same  direction  in 


216 


ELECTRICITY   AND  MAGNETISM. 


all  parts  of  the  coil  that  are  adjacent.  The  attraction  that 
follows  will  cause  the  coil  to  contract  and  lift  one  pole  out  of 
the  mercury  and  break  the  circuit.  The  circuit  broken,  the 
attraction  ceases,  and  the  coil  is  drawn  down  again  by  the  force 
of  gravity,  and  closes  the  circuit  again ;  and  thus  constant 
vibratory  motion  is  produced  in  the  coil. 

Experiment  2.    Prepare  apparatus  as  represented  in  Figure  153. 


Fig.  153. 


Through  a  cork  a,  8cm  in  diameter 
and  5cm  thick,  cut  a  circular  hole 
about  4cm  in  diameter,  and  insert 
a  glass  test-tube  6,  about  6cm 
long,  that  will  just  fit  in  the  hole. 
Takean(No,  20)  insulated  copper 
wire  about  260cm  long,  wind  the 
central  portion  into  a  coil  c,  12cm 
long  and  15mm  in  diameter,  with 
turns  about  3mm  apart,  leaving 
about  12cm  at  both  extremities 
unwound.  To  these  extremities 
solder  strips  of  copper  and  amal- 
gamated zinc  about  3cm  long,  and 
as  wide  as  the  interior  of  the  test- 
tube  will  admit,  and  allow  them 
to  be  separated  about  5mm.  In- 
Fig.  155.  sert  them  in  the  tube, 

and  cover  with  dilute 
sulphuric  acid.  In  the 
center  of  the  coil  lay 
a  No.  16  soft  iron 
wire  d,  and  float  the 
whole  in  a  vessel  of 
water.  The  apparatus 
constitutes  a  small 
floating  battery  and  electro-magnet.  Bring  one  end  of  a  permanent 
magnet,  or  a  short  piece  of  soft  iron  wire  e,  suspended  in  a  paper 
stirrup  w,  near  to  one  of  the  poles  of  the  core  of  the  electro-magnet, 
and  prove  by  experiment  that  the  coil  and  its  core  behave  in  every 
respect  like  a  magnet. 

Experiment  3.    Remove  the  iron  wire  from  the  floating  electro- 


Fig.  154. 


ATTRACTION    OF   CURRENTS.  217 

magnet,  and  bring  a  separate  battery  wire  over  and  parallel  with  the 
helix,  as  in  Figure  154.  In  this  position  the  two  currents  flow  in 
planes  at  right  angles  to  one  another.  Immediately  the  coil  turns  and 
tends  to  take  a  position  at  right  angles  to  the  wire  above,  so  that  the 
two  currents  may  flow  in  parallel  planes  and  in  the  same  direction,  as 
in  Figure  155. 

Hence,  the  Second  Law  of  Currents  :  Angular  currents  tend  to 
become  parallel  and  flow  in  the  same  direction. 

Observe  that  the  action  of  the  Fis-  156- 

helix  in  the  last  experiment  is 
analogous  to  the  deflection  of  a 
magnetic  needle  by  an  electric 
current. 

Experiment  4.  Place  opposite 
one  end  of  the  floating  helix  a  second 
helix,  Figure  156,  in  such  a  manner  that  the  currents  in  the  two  helices 
may  have  the  same  direction.  The  two  poles  of  the  helices  attract 
one  another  in  conformity  to  the  First  Law  of  Currents.  Reverse  the 
poles  of  the  helix  in  your  hand  so  that  the  currents  will  flow  in  oppo- 
site directions,  though  still  parallel;  they  repel  one  another.  (Why?) 

The  two  helices  appear  to  be  polarized  like  two  magnets,  and 
for  many  puiposes  may  be  considered  as  magnets.  Observe 
that  at  one  pole  of  each  helix  the  current  revolves  in  the  direc- 
tion that  the  hands  of  a  watch  move,  and  at  the  opposite  pole 
it  revolves  in  a  direction  contrary  to  the  movement  of  the  hands 
of  a  watch.  Bring  the  north  pole  of  a  bar-magnet  near  that 
pole  of  the  helix  where  the  motion  of  the  current  corresponds  to 
the  movement  of  the  hands  of  a  watch.  The}'  attract  one  an- 
other ;  but  if  the  same  pole  of  the  helix  is  approached  by  the 
south  pole  of  the  magnet,  repulsion  follows.  Hence,  that  is  the 
south  pole  of  a  helix  where  the  current  corresponds  to  the  motion 
of  the  hands  of  a  watch,  (s),  and  that  is  the  north  pole  where  the 
current  is  in  the  reverse  direction,  (N).  But  the  important  les- 
son derived  from  these  latter  experiments  is,  that  helices  through 
which  currents  are  flowing  behave  toward  one  another,  or  toward 
a  magnet,  in  many  respects  as  if  they  were  magnets. 


218 


ELECTRICITY   AND   MAGNETISM. 


§  190.  Ampere's  theory.  —  The  facts  which  we  have  just 
studied  led  Ampere  about  sixty  years  ago  to  devise  a  theory  which 
furnished  a  connecting  link  between  magnetism  and  electricity. 
It  assumed  that  around  every  molecule  of  iron,  steel,  or  other 
magnetizable  substance,  electric  currents  circulate  continuously, 
and  thus  every  molecule  becomes  a  magnet.  According  to  the 
theory,  in  an  unmagnetized  bar  these  currents  lie  in  all  possible 
planes,  and,  having  no  unity  of  direction,  they  neutralize  one 
another,  and  so  their  effect  as  a  system  is  zero.  But  if  a  current 
of  electricity  or  a  magnet  is  brought  near,  the  effect  of  the  in- 
duction is  to  turn  the  currents  into  parallel  planes,  and  in  the 
same  direction,  in  conformity  to  the  Second  Law  of  Currents. 
If  the  coercive  force  is  strong  enough,  this  parallelism  will  be 
attained  on  the  removal  of  the  inducing  cause,  and  a  permanent 
magnet  is  the  result. 

Intensity  of  magnetization  depends  on  the  degree  of  parallel- 
ism, and  the  latter  depends  on  the  strength  of  the  influencing 
magnet.  When  these  currents  have  become  quite  parallel,  the 
body  has  received  all  the  magnetism  that  it  is  capable  of  receiv- 
ing, and  is  said  to  be  saturated.  Although  the  currents  really 

circulate  around  the  individual 
molecules,  yet  the  resultant  of 
these  forces  is  essentially  the 
same  as  if  the  currents  circu- 
lated around  the  body  as  a 
whole.  Figure  157  represents 
sections  of  a  cylindrical  mag- 
net, and  the  included  circles 
the  circulation  of  the  several 
currents  around  the  molecules 
lying  in  these  sections.  It  will 
be  seen  that  the  currents  at  the 
contiguous  sides  of  any  two  of  these  circles  move  in  opposite 
directions,  and  therefore  must  neutralize  one  another  ;  while  the 
currents  that  pass  next  the  circumference  of  the  magnet  are  not 
so  affected. 


N 


AMPERE'S  THEORY. 


219 


The  hypothetical  currents  that  circulate  around  a  magnetic 
molecule  we  shall  call  Ampkrian  currents,  to  distinguish  them 
from  the  known  current  that  traverses  the  helix.  In  strict  accord- 
ance with  this  theory,  the  poles  of  the  electro- magnet  are  deter- 
mined by  the  direction  of  the  current  in  the  helix.  The  inductive 
influence  of  the  electric  current  causes  the  Amperian  currents  to 
take  the  same  direction  with  itself,  as  represented  in  Figure  158. 


Fig.  158. 


N 


However  well  adapted  this  theory  may  be  to  explain  most  of  the 
known  phenomena  of  magnetism,  it  should  be  borne  in  mind 
that  physicists  of  this  generation  value  the  theory  rather  as  a 
help  to  the  imagination  and  memor}',  than  as  a  true  statement 
of  the  facts.  It  is  nearer  the  truth  to  say  that  the  molecules 
are  polarized  as  if  currents  were  circulating  around  them ;  of 
the  actual  existence  of  such  currents  we  know  nothing.  So 
also  of  the  real  nature  of  polarity  we  know  little  or  nothing. 

EXERCISES  AND  QUESTIONS. 

1.  Regarding  your  lead-pencil  as  a  rod  of  iron,  and  a  string  as  an 
electric  wire,  tie  a  knot  at  the  end  where  the  Current  is  supposed  to 
enter  it,  and  wind  the  string  spirally  around  your  pencil,  so  as  to  make 
the  point  of  the  pencil  a  south  pole. 

2.  What  would  be  the  effect  of  reversing  the  current? 


3.  Take  two  tin  mustard-boxes,  and  paint  arrows  around  them,  also 
on  the  ends,  all  turned  in  the  same  direction,  to  represent  Amperian 
currents,  as  in  Figure  159.  Imagine  each  to  be  a  magnet,  determine 


220  ELECTRICITY  AND   MAGNETISM. 

which  is  the  north  and  which  is  the  south  pole  of  each,  and  mark  them 
accordingly  with  the  letters  N  and  S. 

4.  (a)  Place  the  two  south  poles  near  one  another,  and  ascertain 
why  they  should  repel  one  another.     (6)  Do  the  same  with  the  two 
north  poles. 

5.  Let  a  north  and  a  south  pole  face  one  another,  and  show  why 
they  should  attract  one  another. 

6.  Stretch  a  string  in  a  northerly  and  southerly  direction,  and  sus- 
pend one  of  the  boxes  as  a  magnetic  needle  over  and  parallel  with  the 
string,  with  its  north  pole  pointing  north  ;  then  imagine  a  current  to 
enter  the  string  at  its  southern  extremity,  and  determine  its  effects  on 
the  needle. 

7.  Why  is  a  magnetic  needle  deflected  by  an  electric  current? 

8.  Why  is  the  direction  of  the  deflection  dependent  on  the  direction 
of  the  current? 

§  191.  The  earth  a  great  magnet.  —  Experiment  1.  Mag- 
netize a  cambric  needle.  Suspend  it  by  a  fine  thread  attached  to  its 
middle  over  a  magnet,  and  midway  between  its  poles.  The  needle, 
however  placed,  immediately  takes  a  position  parallel  with  the  magnet. 
The  magnet  exerts  a  directive  influence  on  the  needle.  Eemove  the 
magnet,  and  the  needle  takes  a  northerly  and  southerly  direction. 

If  you  carry  the  needle  all  over  your  town  or  State,  it  will  still  main- 
tain this  direction.  Something,  like  the  magnet,  exerts  a  directive 
influence  on  the  magnetic  needle. 

Fig.  160. 


J. 


Experiment  2.  Place  the  needle  once  more  in  its  original  position 
over  the  magnet,  and  gradually  move  it  from  the  middle  towards  one 
pole  of  the  magnet  ;  the  needle  ceases  to  be  horizontal.  At  either  side 
of  the  center  it  dips  ;  if  it  is  nearer  the  N-pole  of  the  bar,  the  S-pole 
dips,  and  conversely,  as  shown  in  Figure  160.  If  the  needle  is  properly 
supported,  the  dip  increases  till  at  the  poles  the  inclination  is  90°. 

If  a  magnetic  needle  freely  suspended  is  carried  to  different 
parts  of  the  earth's  surface,  it  will  dip  as  it  approaches 
the  polar  regions,  and  is  only  horizontal  at  or  near  the  earth's 


THE   EARTH   A    MAGNET. 


221 


Fig.  162. 


equator.  A  common  compass  needle  must  have  the  S-end 
loaded  to  keep  it  horizontal.  Like  effects  are  commonly  at- 
tributed to  like  causes.  These  phenom- 
ena are  just  what  we  should  expect 
if  (as  is  very  improbable)  a  huge  magnet 
were  thrust  through  the  axis  of  rotation 
of  the  earth,  as  represented  in  Figure 
161,  —  having  its  N-pole  near  the  S 
geographical  pole,  and  its  S-pole  near 
the  N  geographical  pole ;  or  if  (as  is 
more  probable)  the  earth  itself  is  a 
magnet. 

Experiment  3.  Magnetize  a  circular  steel  disk,  so  that  its  poles 
may  be  at  the  extremities  of  one  of  its  diameters.  Place  it  beneath  a 
plate  of  glass.  Sift  over 
the  glass  fine  iron-filings, 
as  in  Exp.  2,  p.  28.  Gently 
tap  the  glass  a  few  times, 
so  as  to  agitate  the  filings. 
Once  in  motion,  they  ar- 
range themselves  in  lines 
radiating  from  either  pole, 
forming  graceful  curves 
from  pole  to  pole,  as  rep- 
resented in  Figure  162. 
These  represent  what  are 
called  lines  of  magnetic 
force.  They  represent  the 
resultants  of  the  combined 
action  of  the  two  poles. 
Now  carry  the  little  mag- 
netized cambric  needle 
around  the  disk.  It  follows 
the  lines  of  magnetic  force 
as  mapped  out  by  the  fil- 
ings, always  assuming  a 
position  tangent  to  the  magnetic  curve,  as  shown  in  Figure  162. 


It  is  evident  that  the  space  around  a  magnet  is  the  seat  of  a 


222  KLECTRICITY  AND   MAGNETISM. 

peculiar  influence  ;  this  space,  extending  as  far  as  the  magnet 
exerts  any  effect,  is  called  the  magnetic  field.  The  last  experi- 
ment presents  a  true  exhibition,  on  a  small  scale,  of  what  the 
earth  does  on  a  large  one,  and  thereby  presents  one  of  many 
phenomena  which  lead  to  the  conclusion  that  the  earth  is  a 
magnet. 

§  192.  Magnetic  poles  of  the  earth.  —  It  will  be  seen 
that  there  are  two  points  where  the  needle  points  directly  to  the 
center  of  the  disk.  A  point  was  found  on  the  western  coast  of 
Boothia,  by  Sir  James  Ross,  in  the  year  1831,  where  the  dipping 
needle  lacked  only  one-sixtieth  of  a  degree  of  pointing  directly 
to  the  earth's  center.  The  same  voyager  subsequently  reached 
a  point  in  Victoria  Land  where  the  opposite  pole  of  the  needle 
lacked  only  1°  20'  of  pointing  to  the  earth's  center. 

It  will  be  seen  that,  if  we  call  that  end  of  a  magnetic  needle  which 
points  north  the  N-pole,  we  must  call  that  magnetic  pole  of  the  earth 
which  is  in  the  northern  hemisphere  the  S-pole,  and  vice  versa.  (See 
Fig.  162.)  Hence,  to  avoid  confusion,  many  careful  writers  abstain 
from  the  use  of  the  terms  north  and  south  poles,  and  substitute  for 
them  the  terms  positive  and  negative,  or  marked  and  unmarked  poles. 

§  193.  Variation  of  the  needle.  —  Inasmuch  as  the  mag- 
netic poles  of  the  earth  do  not  coincide  with  the  geographical 
poles,  it  follows  that  the  needle  does  not  in  most  places  point  due 
north  and  south.  The  angle  which  the  needle  makes  with  the 
geographical  meridian  is  known  as  the  angle  of  declination. 
This  angle  differs  at  different  places. 

Experiment.  As  Columbus  found,  we  can  easily  find,  the  declina- 
tion at  any  place  as  follows :  Set  up  two  sticks  so  that  a  string  joining 
them  points  to  the  North  Star ;  the  string  will  lie  in  the  geographical 
meridian.  Place  a  long  magnetic  needle  over  the  string;  the  angle 
between  the  needle  and  the  string  is  the  required  declination.  If  great 
accuracy  is  required,  allowance  must  be  made  for  the  fact  that  the 
star  is  not  exactly  over  the  pole,  but  appears  to  describe  daily  around 
it  a  circle  whose  diameter  is  about  4°. 


VARIATION   OF   THE   NEEDLE.  223 

Let  A  (Fig.  163)  represent  a  magnetic  pole,  and  B  the  North 
Star ;  it  will  be  seen  that  there  is  a  posi-  Fig.  163. 

tion  in  which  the  needle  will  point  due 
north.  A  line  passing  around  the  earth 
through  the  two  magnetic  poles,  con- 
necting those  places  where  the  needle 
points  due  north,  is  called  a  line  of  no 
variation.  On  the  map,  Plate  II.,  it  is  marked  0.  Lines  east 
and  west  of  this  line,  and  approximately  parallel  with  it,  repre- 
sent lines  of  equal  variation.  At  places  in  the  United  States 
east  of  this  line  the  needle  points  west  of  north,  e.g.,  New 
England ;  but  most  of  the  States  lie  west  of  this  line,  so  in  them 
the  needle  points  east  of  north. 

The  magnetic  poles  are  not  fixed  objects  that  can  be  located 
like  an  island  or  cape,  but  are  constantly  changing.  They  ap- 
pear to  swing,  somewhat  like  a  pendulum,  in  an  easterly  and 
westerly  direction,  each  swing  requiring  centuries  to  complete  it. 
The  north  magnetic  pole  is  now  on  its  westerly  swing.  The 
chart  given  in  this  book  was  only  true  at  the  time  of  observation 
in  1870.  To  be  true  for  the  present  time,  each  of  the  lines 
should  be  moved  westward  at  the  rate  of  about  1°  for  every 
twelve  years. 

§  194.  Natural  magnets.  —  On  the  assumption  that  the 
earth  is  a  magnet,  it  would  not  be  strange  if  magnetizable  sub- 
stances should  partake  of  its  magnetic  properties  by  induction. 
An  ore  of  iron  called  lodestone,  composed  of  a  mixture  of  two 
oxides  of  this  metal,  possesses  more  or  less  magnetic  power. 
Such  magnets  are  termed  natural  magnets,  to  distinguish  them 
from  the  artificial  magnets  of  steel. 

§  195.  Cause  of  the  earth's  magnetism.  —  The  cause  of 
the  earth's  magnetism  is  not  known.  The  theory  that  it  is  an 
electro-magnet  in  virtue  of  currents  flowing  around  it  near  its 
surface,  from  east  to  west,  explains  all  the  effects  that  it  pro- 
duces on  the  magnetic  needle.  But  what  sustains  these  electric 


224  ELECTRICITY   AND   MAGNETISM. 

currents?  There  are  many  things  that  point  to  the  sun  as  the 
source  of  the  earth's  magnetism.  Those  who  adopt  this  theorj 
generally  regard  the  terrestrial  currents  as  thermo-electric. 

A  single  instance  must  suffice  to  illustrate  the  intimate  relation  thai 
certainly  exists  between  the  sun's  condition  and  the  earth's  mag- 
netism. In  1859  two  observers  remote  from  each  other  saw  simul 
taneously  a  bright  spot  break  out  on  the  face  of  the  sun,  whose  duratioc 
was  only  five  minutes.  Exactly  at  this  time  there  was  a  general  dis- 
turbance of  magnetic  needles,  and  telegraph  wires  all  over  the  worlc 
were  traversed  with  so-called  earth  currents.  Telegraphers  received 
shocks,  and  an  apparatus  in  Norway  was  set  on  fire.  These  phenomena 
were  quickly  followed  by  auroral  displays.  Sometimes  telegraphs  are 
worked  by  earth  currents  alone,  without  any  battery  in  the  circuit. 

§  196.  General  remarks  on  magnets  and  magnetism, 
—  Artificial  magnets,  including  permanent  magnets  and  electro- 
magnets, are  usually  made  in  the  shape  either  of  a  straight  bar 
or  of  the  letter  U,  called  the  horse-shoe,  according  to  the  use 
made  of  them.  If  we  wish,  as  in  the  experiments  already  de- 
scribed, to  use  but  a  single  pole,  it  is  desirable  to  have  the  other 
as  far  away  as  possible  ;  then  obviously  the  bar-magnet  is  most 
convenient.  But  if  the  magnet  is  to  be  used  for  lifting  or  hold- 
ing weights,  the  horse-shoe  form  is  far  better,  because  the 
FI  164  attraction  of  both  poles  is  conveniently  available, 
and  because  their  combined  power  is  more  than 
twice  that  of  a  single  pole.  This  is  due  to  the 
reflex  influence  of  the  poles  on  one  another  through 
the  armature.  Magnets,  when  not  in  use,  ought 
alwa}'s  to  be  protected  by  armatures  (A,  Fig.  164) 
of  soft  iron ;  for,  notwithstanding  the  coercive 
power  of  steel,  they  slowly  part  with  their  magne- 
tism. But  when  an  armature  is  used,  the  opposite 
poles  of  the  magnet  and  armature  being  in  contact 
with  one  another,  i.e.,  N  with  S,  they  serve  to  bind 
one  another's  magnetism. 

Thin  bars  of  steel  can  be  more  thoroughly  magnetized  than 


Plate  II. 


DIAMAGNETISM.  225 

thick  ones.  Hence,  if  several  thin  bars  (Fig.  164)  are  laid  side 
by  side,  with  their  corresponding  poles  turned  in  the  same 
direction,  and  then  screwed  together,  a  very  powerful  magnet 
is  the  result.  This  is  called  a  compound  magnet.  In  any  mag- 
net the  outer  layers  are  far  more  strongly  magnetized  than  the 
central  ones ;  so  a  steel  tube  makes  very  nearly  as  strong  a 
magnet  as  a  rod  of  the  same  diameter,  and  is  much  lighter  than 
the  latter. 

§  197.  Diamagnetism.  —  Besides  iron  and  steel,  many 
other  substances,  and  possibly  all  substances,  both  in  the  liquid 
and  gaseous,  as  well  as  in  the  solid  state,  are  more  or  less  sus- 
ceptible to  magnetic  influence.  Conspicuous  among  these  are 
nickel  and  cobalt.  But  this  influence  is  not  always  of  the  same 
kind.  A  small  bar  of  bismuth  suspended  between  the  poles  of 
a  powerful  electro-magnet,  instead  of  being  attracted  is  repelled 
by  the  poles  of  the  magnet,  as  shown  by  its  taking  a  position 
with  its  longest  axis  at  right  angles  to  a  direct  line  between  the 
poles.  Substances  which  behave  in  this  manner  are  called  dia- 
magnetic, and  they  are  said  to  place  themselves  equatorially 
between  the  poles.  Substances  that  place  themselves  axially 
between  the  poles,  as  iron  and  nickel,  are  called  paramagnetic, 
or  simply  magnetic. 

Paramagnetic  liquids  placed  in  a  watch-glass  between  the 
poles  become  heaped  up  at  the  poles  and  depressed  in  the  cen- 
ter, while  the  opposite  phenomena  occur  with  diamagnetic 
liquids.  The  magnetic  behavior  of  gases  may  be  learned  by 
inflating  soap-bubbles  with  them,  and  noting  the  direction  of 
their  distension.  Alcohol,  water,  nitrogen,  and  carbonic  acid 
are  diamagnetic.  Oxygen  is  paramagnetic.  The  only  sub- 
stances whose  magnetic  properties  can  be  shown  without  extra- 
ordinary apparatus  are  iron  and  its  compounds. 

§  198.  Magnets  not  sources  of  energy.  —  Perpetual- 
motion  seekers  are  easily  led  into  the  error  of  supposing  that  in 
the  magnet  they  have  an  inexhaustible  supply  of  energy ;  but 


226  ELECTRICITY   AND   MAGNETISM. 

a  very  little  study  will  serve  to  exhibit  the  character  of  the 
error.  If,  for  instance,  we  bring  a  piece  of  iron  near  a  magnet, 
it  is  attracted,  and,  if  allowed  to  move  up  to  the  magnet,  this 
force  of  attraction  will  do  a  certain  amount  of  work.  Take  now 
another  piece  of  iron  similar  to  the  first ;  this  also  will  be  at- 
tracted, and  a  certain  amount  of  work  will  be  performed,  but  a 
less  amount  than  that  done  in  the  first  instance.  Continue  the 
operation  until  the  magnet  no  longer  attracts  ;  then  the  magnet 
has  done  a  definite  amount  of  work,  and  lost  the  power  of  doing 
more.  To  restore  it  to  its  original  condition,  we  must  remove 
all  the  pieces  of  iron  ;  this  will  require  an  expenditure  of  exter- 
nal work  exactly  equal  to  that  originally  performed  by  the 
magnet. 

XXXII.     MAGNETO-ELECTRIC   AND  CURRENT  INDUCTION. 

§  199.  Introductory  experiments.  —  Experiment  1.  Con- 
nect a  helix  with  a  delicate  galvanometer  (Fig.  165),  and  quickly  thrust 
a  magnetized  steel  rod  into  the  coil.  A  deflection  of  the  needle  shows 
that  a  current  of  electricity  at  that  instant  traverses  the  wire.  But 

the  needle,   after   a  few  oscilla- 

r ig.  loo. 

tions,  assumes  its  original  posi- 
tion. This  shows  that  the  current 
was  only  momentary.  Quickly 
remove  the  magnet ;  again  the  wire 
is  traversed  by  a  current,  but  this 
time  in  an  opposite  direction  to 
the  first,  as  shown  by  an  opposite 
deflection.  Repeat  the  experiment, 
and  notice  that  when  the  magnet 
approaches  the  coil  the  induced 
current  runs  in  the  opposite  direc- 
tion to  the  Amperian  currents,  as 
represented  in  Figure  166.  But 
when  the  magnet  is  withdrawn, 
the  induced  current  takes  the  same  direction  with  the  Amperian  cur- 
rents, as  in  Figure  167.  In  the  former  case,  the  repulsion  due  to 
opposite  currents  must  act  as  a  resistance  to  the  force  that  brings  them 


MAGNETO   AND    DYNAMO   MACHINES. 


227 


Yig.  166. 


Fljf.  167. 


together.  Likewise,  in  the  latter  case,  the  attraction  due  to  currents 
flowing  in  the  same 
direction  must  resist 
the  force  that  sepa- 
rates them.  Hence, 
the  energy  shown  by 
the  electric  current  has 
been  generated  at  the 
expense  of  mechanical 
energy. 

Experiment  2. 
Place  within  the  coil 
a  core  of  soft  iron.  Wave  back  and  forth,  over  one  extremity  of  the 
core,  one  of  the  poles  of  a  powerful  bar-magnet.  The  needle  of  the 
galvanometer  is  violently  agitated,  being  deflected  in  one  direction  at 
each  approach,  and  in  the  opposite  direction  at  each  departure.  Now 
repeat  the  experiments  with  the  opposite  pole  of  the  magnet.  The 
effect  is,  as  we  should  expect,  to  reverse 
all  the  currents. 


Fig.  168. 


§  200.  Magneto  and  dynamo 
machines.  —  If  the  permanent  mag- 
net is  stationary,  and  the  electro- 
magnet is  moved  back  and  forth, 
the  result  is  the  same  as  when  the 
magnet  was  moved  and  the  electro- 
magnet was  stationary.  Machines 
constructed  for  the  purpose  of  gene- 
rating electric  currents  in  this  manner 
are  called  magneto-electrical  machines. 

Figure  168  will  give  a  general  idea  of 
the  construction  of  the  simpler  kinds  of 
magneto  machines.  N  S  is  a  permanent 
compound  horse-shoe  magnet.  E  E  are 
coils  containing  cores  of  soft  iron  con- 
nected by  the  back-armature  C  C,  the 
whole  constituting  a  sort  of  an  armature 

to  the  permanent  magnet.     The  brass  axle  D  T)  is  rigidly  connected 
with  the  back-armature  C  C,  so  that  when  the  axle  is  rotated  by  means 


228 


ELECTRICITY   AND   MAGNETISM. 


of  the  crank  A,  both  helices  are  carried  around  with  it.  Now,  suppose 
the  crank  to  be  turned ;  during  the  first  quarter  of  a  revolution  a  sep- 
aration of  poles  occurs,  and  currents  of  electricity  are  established  in 
both  helices.  The  wire  that  constitutes  the  helix  is  wound  in  opposite 
directions  around  the  two  cores,  so  that  the  two  currents  may  not  flow 
in  opposite  directions  through  the  wire,  and  thereby  neutralize  one  an- 
other, but  may  have  a  common  direction,  and  thereby  produce  a  current 
of  double  the  electro-motive  force  that  would  be  produced  in  a  single 
helix.  During  the  second  quarter-revolution  the  poles  approach  one  an- 
other, and  the  effect  would  be  to  reverse  the  current ;  but  the  polarity  of 
the  cores  also  change  as  they  are  now  brought  under  the  influence  of  the 
poles  which  they  are  approaching,  and  this  double  change  leaves  the  cur- 
rent to  flow  in  the  same  direction  as  it  did  before.  At  the  end  of  a  half 
revolution  there  is  a  reversal  of  current,  as  the  poles  do  not  change  at 
this  point.  The  result  would  be  that  during  every  revolution  there 
would  be  a  current  half  of  the  time  in  one  direction,  and  half  of  the 
time  in  the  opposite  direction.  In  order  to  secure  a  constant  current 
in  one  direction,  a  current-reverser  I,  or  commutator,  as  it  is  called,  at- 
tached to  the  axle,  is  so  arranged  that  the  current  is  reversed  at  the 
end  of  each  half  revolution,  and  is  then  conducted  away  by  the  wires 
GH. 

Each  of  the  two  currents  produced  in  a  single  revolution  has  a 

maximum  point,  or  point  of 
greatest  intensity,  when  the 
cores  are  nearest  the  poles  of 
the  magnet;  and  a  minimum 
point,  or  point  of  least  intensity, 
when  they  are  farthest  from  the 
poles.  Between  these  two 
points  the  current  is  constantly 
growing  or  diminishing.  It  is 
apparent  that  such  a  machine 
gives  not  only  an  intermittent 
current,  but  one  that  resembles 
a  succession  of  waves  or  a 
stream  produced  by  the  strokes 
of  a  pump,  alternately  rising 
and  sinking.  But  for  most 
purposes  for  which  electricity  is  employed,  it  is  important  that  the 
current  should  be  continuous  and  uniform.  Figure  160  will  serve  to 
illustrate  the  principle  by  which  this  is  secured  in  the  widely-known 
Gramme  machine. 


MAGNETO   AND   DYNAMO   MACHINES.  229 

The  armature  ns  consists  of  a  ring  composed  of  a  bundle  of  soft 
iron  wires  (better  shown  in  Fig.  169  a)  surrounded  by  what  is  virtually 
an  endless  coil  of  wire.  The  wire,  however,  is  put  on  in  separate 
coils,  the  in-wire  of  one  united  to  the  out- wire  of  the  next,  and  from 
each  junction  a  branch  wire  is  led  to  a  copper  plate  on  the  axis  of 
rotation  mm.  A  horse-shoe  magnet  NS  (only  a  portion  of  which  is 
shown  in  the  cut)  is  so  placed  that  one-half  of  the  ring  is  under  the 
influence  of  the  N-pole,  and  the  other  half  under  that  of  the  S-pole. 
Suppose  the  ring  to  rotate  in  the  direction  of  the  arrow ;  then  every 
point  of  the  iron  core,  as  it  comes  opposite  a  given  point  of  the 
magnet,  will  successively  become  a  pole  of  opposite  name,  while  the 
points  i  and  i'  are  the  neutral  points.  If  we  imagine  the  core  to  be 
divided  at  the  points  n  and  s,  we  have  two  semicircular  magnets  whose 
north  poles  and  whose  south  poles  respectively  face  one  another.  In 
the  two  mutually-facing  poles  on  either  side,  the  Amperian  currents 
must  be  in  opposite  directions.  Now  an  attentive  study  of  this  ideal 
diagram  in  the  light  of  what  you  have  previously  learned  respecting 
the  generation  of  induced  currents  will  enable  you  to  see  that  as  the 
ring  armature  rotates,  the  corresponding  advance  of  the  induced  poles 
of  the  ring  will  induce  currents  in  the  wire  in  such  a  manner  that  all 
the  coils  which  at  any  given  moment  are  in  the  semicircle  next  one  of 
the  magnet  poles  —  say  the  North  —  are  traversed  by  a  current  of  one 
direction.  Similarly,  the  semicircle  formed  by  the  coils  immediately 
approaching,  or  immediately  receding  from  the  South  pole  are  at  the 
same  time  traversed  by  a  current  of  the  opposite  direction.  The  result 
is  that  currents  in  the  lower  half  tend  toward  the  point  m  on  the  axis, 
and  in  the  upper  half  from  point  m'.  So  long  as  the  leading  out-wires 
from  these  points  are  open,  these  currents  have  no  outlet,  and  conse- 
quently oppose  and  neutralize  one  another.  But  if  the  points  m  and 
m'  are  connected  by  a  wire  L,  we  shall  have  a  constant  and  non-alternat- 
ing current  flowing  through  the  wire  from  m  to  m'.  The  contact  at 
these  points  is  made  by  means  of  brushes  of  thick  wire  provided  as 
springs.  These  press  on  the  contact  pieces  and  make  practically  a 
constant  connection  with  the  two  halves  of  the  circuit. 

Inasmuch  as  an  electro-magnet  may  be  made  a  much  more  powerful 
magnet  than  a  permanent  magnet,  it  is  now  extensively  used  as  the 
inducing  or  the  so-called  field  magnet.  Such  a  machine  is  called  a 
dynamo-electrical  machine,  or  often  more  briefly  a  dynamo.  Figure 
1G9  b  represents  such  a  machine.  EE  is  the  stationary  field  magnet, 
A  the  moving  armature,  and  N  and  S  large  pole-pieces  brought  as 
near  as  practicable  to  the  armature  and  partially  encircling  it.  When 


230 


ELECTKIC1TY   AND   MAGNETISM. 


the  machine  is  at  rest,  there  are  no  currents ;  but  when  the  armature  is 
in  motion,  the  residual  magnetism  (a  small  portion  of  the  magnetism 
which  soft  iron  always  retains  after  it  has  been  magnetized)  induces 
at  first  a  weak  current  in  the  wire  of  the  armature;  but  as  a  portion  of 
this  current  is  carried  by  means  of  a  shunt  wire  I  through  the  coil  of 
the  field  magnet,  and  magnetizes  the  core  more  and  more  strongly, 
the  current  in  both  the  shunt  I  and  the  main  wire  L  quickly  reaches 
its  maximum. 

By  the  kind  permission  of  the  United  States  Electric  Lighting 
Company  we  introduce  a  cut,  Fig.  169  c,  of  the  popular  American 
dynamo  called  the  Weston.  It  will  be  seen  that  in  this  machine  two 
powerful  field  magnets  are  placed  one  on  either  side  of  the 
revolving  armature.  Power  originated  in  a  steam  engine  is  com- 
municated to  the  dynamo  by  means  of  a  belt  passing  over  the  circum- 
ference of  the  wheel  W  and  causes  the  armature,  which  is  on  the  axle 
of  this  wheel,  to  revolve. 

§  201.  Current  induction.  —  If,  in  the  original  experiment 
in  magneto-electric  induction  (p.  226),  a  helix  connected  with  a 
battery  is  substituted  for  the  permanent  magnet,  precisely  the 
same  results  are  obtained  as  with  the  magnet.  Indeed,  we  ought 
to  expect  the  same  results.  (Why?)  The  wire  A,  Figure  170, 


Fig.  170. 


through  which  the  battery  current  circulates,  is  known  in  this 
case  as  the  primary  wire,  and  the  battery  current,  the  primary 
or  inducing  current.  The  wire  B,  through  which  the  induced 
currents  circulate,  is  called  the  secondary  wire,  and  the  currents 
that  traverse  this  wire  are  frequently  called  secondary  currents. 


Fig.  169  c. 


k 


EXTRA   CURRENT.  231 

It  will  be  observed  that  in  all  these  experiments  we  have  a 
relative  motion  between  a  conductor  and  an  inducing  body 
(magnet  or  current-bearing  conductor)  ;  also,  that  electricity 
flows  only  during  the  continuance  of  the  relative  motion.  Deli- 
cate measurements  have  proved  that  the  total  quantity  of 
induced  electricity  transmitted  in  the  conductor  depends  on 
the  total  quantity  of  change  in  relative  motion,  and  not  at  all 
on  the  time  occupied  in  this  change.  Hence,  it  is  evident,  that 
the  more  rapid  the  change,  the  more  intense  must  be  the  momen- 
tary current;  i.e.,  the  greater  must  be  the  quantity  of  electri- 
city flowing  at  the  moment.  Combining  this  statement  with 
Ohm's  law,  remembering  that  the  resistance  of  the  secondary 
circuit  is  constant,  we  derive  the  following  very  important  law : 
In  any  induced  current,  the  E.M.F.  at  any  instant  is  propor- 
tional to  the  rapidity  of  the  relative  change  at  that  instant. 

If,  instead  of  bobbing  the  primary  helix  in  and  out  of  the  secondary 
helix,  the  former  is  allowed  to  remain  stationary  within  the  latter,  it  is 
found  that  making  and  breaking  (Fig.  170)  the  primary  current,  i.e., 
starting  and  stopping  a  primary  current,  induces  currents  in  the  secon- 
dary wire.  Indeed  this  process  is  evidently  much  the  same  thing  (and 
in  theory  exactly  the  same  thing),  as  moving  the  primary  conductor, 
with  unbroken  circuit,  from  an  infinite  distance  where  its  action 
would  be  zero,  into  the  secondary  circuit,  the  whole  change  occupying 
a  very  brief  time.  A  reversal  of  the  process  would  evidently  corre- 
spond to  breaking  the  primary  circuit.  The  results  obtained  in  Exp.  1, 
§  197,  enable  us  at  once  to  predict  the  direction  of.  an  induced  current, 
and  we  may  formulate  the  two  cases  thus :  — 

(a)  When  the  primary  current  is  approached,  or  a  current  originated  in 
the  primary  circuit,  the  induced  current  has  an  opposite  direction  to  that 
of  the  primary. 

(6)  At  a  departure  from  the  primary  current,  or  when  a  current  in  a 
primary  circuit  is  stopped,  the  induced  current  has  the  same  direction  as 
the  primary. 

§  202.  Extra  current.  —  The  conclusions  of  the  preceding 
section  admit  of  an  important  extension.  We  learned  that  any 
electric  or  magnetic  disturbance  in  the  neighborhood  of  a  con- 


232  ELECTBICITY  AND  MAGNETISM. 

ductor  gives  rise  to  a  current.  But  it  is  evident  that  in  a  single 
wire  every  portion  must  be  considered  as  a  neighboring  conduc- 
tor with  respect  to  every  other  portion  ;  consequently  there  can 
be  no  change  of  electrical  condition  in  a  wire  without  accom- 
panying induction  phenomena.  If  we  suddenly  close  a  circuit 
the  current  does  not  abruptly  assume  its  final  intensity,  because 
there  is  a  current  induced  in  the  same  circuit  whose  direction  is 
such  as  to  retard  the  change  from  zero.  So,  too,  if  a  closed 
circuit  be  suddenly  broken,  there  is  a  current  induced  in  the 
direction  of  the  primary  current  which  retards  the  change  to 
zero.  These  induced  currents  are  often,  for  the  sake  of  dis- 
tinction, called  extra  currents.  Of  course,  if  all  parts  of  the  con- 
ductor are  kept  close  together  by  winding  the  wire  into  a  helix 
or  a  spiral,  the  effect  is  much  increased.  It  is  evident  that  the 
direct  extra  current  must  produce  a  much  greater  effect  than 
the  indirect,  because  the  former  is  added  to  the  primary,  while 
the  latter  is  subtracted.  This  is  the  cause  of  the  bright  spark 
on  breaking  a  strong  current,  and  also  of  physiological  effects 
or  shocks  experienced  on  breaking  the  primary  circuit  in  the 
experiment  illustrated  by  Figure  170.  If  a  soft  iron  core  is 
introduced  into  a  helix,  the  extra  currents  are  vastly  increased 
by  the  action  of  the  magnetic  changes.  (Why?) 

§  203.  Induction  coils.  —  If  a  core  of  iron,  or,  still  better, 
a  bundle  of  wires  (A  A,  Fig.  171),  is  inserted  in  the  primary 
coil,  it  is  evident  that  it  will  be  magnetized  and  demagnetized 
every  time  the  primary  is  made  and  broken.  The  starting  and 
cessation  of  Amperian  currents  in  the  core  in  the  same  direction 
as  the  primary  current,  and  simultaneous  with  the  commence- 
ment and  ending  of  the  primary  current,  greatly  intensifies  the 
secondar}7  current.  To  save  the  trouble  of  making  and  break- 
ing by  hand,  as  in  Figure  171,  the  core  is  also  utilized  in  the 
construction  of  an  automatic  make-and-break  piece.  A  soft 
iron  hammer  b  is  connected  with  the  steel  spring  c,  which  is  in 
turn  connected  with  one  of  the  terminals  of  the  primary  wire. 


RUHMKQBFF  S  COIL. 


233 


The  hammer  presses  against  the  point  of  a  screw  d,  and  thus, 
through  the  screw,  closes  the  circuit.  But  when  a  current 
passes  through  the  primary  wire,  the  core  becomes  magnetized, 
draws  the  hammer  away  from  the  screw,  and  breaks  the  circuit. 


Fig.  171. 


The  circuit  broken,  the  core  loses  its  magnetism,  and  the  hammer 
springs  back  and  closes  the  circuit  again.  Thus  the  spring  and 
hammer  vibrate,  and  open  and  close  the  primary  circuit  with 
great  rapidity.  An  instrument  made  on  these  principles  is 
called  an  induction  coil. 

§  204.  Ruhmkorff's  coil.  —  This  instrument  has  the  impor- 
tant addition,  to  the  parts  already  explained,  of  a  condenser  BB. 
This  consists  of  two  sets  of  layers  of  tinfoil  separated  by  paraf- 
fine  paper ;  the  layers  are  connected  alternate!}'  with  one  and 
the  other  pole  of  the  battery,  as  the  figure  shows,  so  that  they 
serve  as  a  sort  of  expansion  of  the  primary  wire.  When  the 
circuit  is  broken,  the  extra  current  would  jump  across  at  6,  and 
would  vaporize  the  points  of  contact,  and  form  a  bridge  with  the 
vapor  of  metal  that  would  prolong  the  time  of  breaking.  But, 


234  ELECTKICITY   AND   MAGNETISM. 

when  the  condenser  is  attached,  the  extra  current  finds  an 
escape  into  it  easier  than  to  jump  across  at  6,  so  the  vaporizing 
of  the  contact  is  avoided,  and  the  time  of  breaking  being  much 
shortened,  the  secondary  is  much  more  intense. 

The  primarj'  helices  of  induction  coils  consist  of  comparatively 
few  turns  of  coarse  insulated  wire  ;  but  the  secondary  helices 
contain  many  turns  of  very  fine  wire,  insulated  with  great  care. 
The  secondary  current  is,  at  breaking,  as  we  ought  to  expect 
from  the  extreme  rapidity  with  which  the  primary  circuit  is 
broken,  distinguished  from  the  primary,  or  galvanic  current,  by 
its  vastl}'  greater  tension,  or  power  to  overcome  resistances. 
A  coil  constructed  for  Mr.  Spottiswoode  of  London  has  two 
hundred  and  eighty  miles  of  wire  in  its  secondary  coil.  With 
five  Grove  cells  this  coil  gives  a  secondary  spark  forty-two  inches 
long,  and  perforates  glass  three  inches  thick.  Many  brilliant 
experiments  may  be  performed  with  these  coils  which  will  be 
indicated  in  connection  with  frictional  machines. 


XXXIII.     THERMO-ELECTRICITY. 

§  205.  So  far  in  our  experiments  we  have  obtained  a  current 
of  electricity  by  using  the  potential  energy  due  to  the  chemical 
affinity  of  zinc  and  sulphuric  acid,  or  by  expending  mechanical 
energy ;  can  we  not  also  get  a  current  directly  from  the  molec- 
ular energy  that  we  know  as  heat? 

Experiment.  Insert  in  one  screw  cup  of  a  sensitive  galvanometer 
an  iron  wire,  and  in  the  other  cup  a  copper,  or,  better,  a  German  silver 
wire.  Twist  the  other  ends  of  the  wire  together,  and  heat  them  at 
their  junction  in  a  flame ;  a  deflection  of  the  needle  shows  that  a  cur- 
rent of  electricity  is  traversing  the  wire.  Place  a  piece  of  ice  at  their 
junction.  A  deflection  in  the  opposite  direction  shows  that  a  current 
now  traverses  the  wire  in  the  opposite  direction. 

These  currents  are  named,  from  their  origin,  thermo-electric. 
The  apparatus  required  for  the  generation  of  these  currents  is 
very  simple,  consisting  merely  of  bars  of  two  different  metals 


THERMO-ELECTRICITY. 


235 


joined  at  one  extremit}',  and  some  means  of  raising  or  lowering 
their  temperature  at  their  junction,  or  of  raising  the  temperature 
at  one  extremit}*  of  the  pair  and  lowering  it  at  the  other  ;  for  the 
electro-motive  force,  and  consequently  the  strength  of  the  cur- 
rent, is  nearly  proportional  to  the  difference  in  temperature  of 
the  two  extremities  of  the  pair.  The  strength  of  the  current  is 
also  dependent,  as  in  the  voltaic  pair,  on  the  thermo-electro- 
motive  force  of  the  metals  employed.  The  following  thermo- 
electric series  is  so  arranged  that  if  the  temperatures  of  both 
junctions  are  near  the  ordinary  temperatures  of  the  air,  those 
metals  farthest  removed  from  each  other  give  the  strongest  cur- 
rent when  combined ;  and  the  current  passes,  when  heated  at 
their  junction,  from  the  one  first  named  to  that  succeeding  it. 
The  arrows  indicate  the  direction  of  the  current  at  the  heated 
and  cold  ends  respectively.  At  high  temperatures  the  current 
may  be  reversed. 

«:  Cold. 


O 


.2      g     .S 

Jzj      5      H 


.  s 

I  I  I!  ••  4 

&  3  5  I 

O  Pn  cfi  S3 


2    5 

I-H          <1 


Heat. 


Fig.  172. 
HEAT 


§  206.  Thermo-electric  batteries  and  thermo-pile.  — 
The  electro-motive  force  of  the  thermo-electric  pair  is  very 
small  in  comparison  with  that  of  the  voltaic  pair ; 
hence  the  greater  necessity  of  combining  a  large 
number  of  pairs  with  one  another  in  series.  This 
is  done  on  the  same  principle,  and  in  the  same 
manner,  that  voltaic  pairs  are  united,  viz.,  by  join- 
ing the  +  metal  of  one  pair  to  the  —metal  of  an- 
other. Figure  172  represents  such  an  arrange- 
ment. The  light  bars  are  bismuth,  and  the  dark 
ones  antimony.  If  the  source  of  heat  is  strong 
and  near,  by  either  conduction  or  convection  one  face  may  be 


COLD 


236  ELECTRICITY  AND  MAGNETISM. 

heated  much  hotter  than  the  other,  and  a  current  equal  to  that 
from  an  ordinary  galvanic  cell  is  often  obtained.  Instruments 
constructed  on  these  principles,  and  used  as  a  source  of  elec- 
tricity, are  very  convenient  and  efficient  for  many  purposes, 
especially  when  a  steady  current  is  required  with  small  external 
resistance  ;  they  are  called  thermo-electric  batteries. 

If  the  source  of  heat  is  feeble  or  distant,  the  feeble  current 
may  serve  to  measure  the  difference  of  temperature  between  the 
ends  of  the  bars  turned  toward  the  heat  (as  in  Figure  172) 
and  the  other  ends,  which  are  at  the  temperature  of  the  air. 
The  apparatus,  when  used  for  this  purpose,  is  called  a  thermo- 
pile, or  a  thermo-multiplier .  A  combination  of  as  many  as 
thirty-six  pairs  of  antimony  and  bismuth  bars,  connected  with 
a  very  sensitive  galvanometer,  constitutes  an  exceedingly  deli- 
cate thermoscope  and  thermometer.  Quantities  of  heat,  that 
would  not  perceptibly  expand  the  mercury  in  an  ordinary  ther- 
mometer, can,  by  the  use  of  a  thermo-electric  pile,  be  made  to 
produce  large  deflections  of  the  galvanometer  needle.  Heat 
radiated  from  the  body  of  an  insect  several  inches  from  the  pile 
may  cause  a  sensible  deflection. 


MECHANICAL  ENERGY. 


237 


XXXIV.     FRICTIONAL    ELECTRICITY. 

§  207.  Mechanical  energy  transformed  into  electrifi- 
cation.—  Experiment.  Prepare  an  insulated  stool  (see  §  214)  by 
placing  a  square  board  on  four  dry  and  clean  glass  tumblers,  used  as 
legs.  Let  a  person  whom  we  will  call  John  stand  on  this  stool,  and 
let  a  second  person, 

James,    strike    John,  a  Fig.  173. 

few  times  with  a  cat's 
fur.  Then  let  James 
bring  a  knuckle  of  a 
finger  near  to  some  part 
of  John's  person,  for 
instance  a  knuckle  of 
his  hand,  or  his  chin  or 
nose ;  an  electric  spark 
will  pass  between  the 
two,  and  both  will  expe- 
rience a  slight  shock. 
The  length  of  the  spark 
shows  that  the  electri- 
city is  urged  by  a  high 
E.M.F.,  like  the  induced 
currents  of  the  magneto-machine  and  induction  coil. 

As  mechanical  energy  is  transformed  into  a  kind  of  molecular 
motion,  or  internal  energy,  called  heat,  when  one  hammers  an 
anvil,  so  in  this  case  a  portion  of  the  motion  of  the  fur  at  each 
stroke  is  transformed  into  another  phase  of  internal  energy  known 
as  electrification.  Electricity  made  apparent  in  this  manner  is 
called  fractional  electricity,  because  the  electrification  Fig.  174 
is  developed  by  friction  between  two  surfaces. 

§  208.  Electroscope. — Experiment.  Suspend  in 
a  loop,  tied  in  a  white  silk  thread,  a  strip  of  gold  foil  20cm 
long  and  15mm  wide,  so  that  the  two  vertical  portions  may 
be  near  each  other.  After  John  has  been  struck  a  few 
times  with  the  fur,  let  him  bring  a  finger  gradually  near  the  upper  ex- 
tremity of  the  foil;  the  two  portions  of  the  foil  gradually  diverge, 
as  in  Figure  174,  indicating  the  presence  of  an  unusual  force  in  his  body. 


238 


ELECTRICITY  AND   MAGNETISM. 


We  have  already  found  that  this  force  is  due  to  electricity. 
Bodies  in  this  state  are  said  to  be  charged  with  electricity,  or 
simply  electrified.  Such  electrification  in  a  person  is  often 
manifested  by  a  divergence  of  hair  on  his  head.  Any  ar- 
rangement, like  that  of  the  foil  just  described,  intended  to 
detect  the  presence  of  electrification,  is  called  an  electroscope. 
One  of  the  most  common  and  useful  electroscopes  consists 
of  one  or  two  pith-balls,  made  from  the  pith  of  elder  or 
sunflower,  suspended  by  silk  thread.  If  an  electroscope  is 
brought  near  to  either  pole  of  a  secondary  wire  of  an  induction 
coil,  a  similar  electrification  is  manifested  by  the  poles.  Like- 
wise, by  means  of  very  delicate  electroscopes,  the  poles  of  a 
galvanic  battery,  or  of  a  thermo-battery,  are  found  to  be  feebly 
electrified. 

§  209.  Attractions  and  repulsions.  —  Experiment  1.  Poise 
a  flat  wooden  ruler  on  an  inverted  bottle  or  flask,  having  a  round  bot- 
tom, as  in  Figure  175.  Draw  a  rubber  comb  two  or  three  times  through 

your  hair,  or  rub  it  with  a  woolen  cloth, 
and  place  it  near  one  end  of  the  ruler ; 
instantly  the  ruler  moves  toward  the 
comb. 

Experiment  2.  Hold  the  comb  over 
a  handful  of  bits  of  tissue  paper ;  the 
papers  quickly  jump  to  the  comb,  stick 
to  it  for  an  instant,  and  then  leap  ener- 
getically from  the  comb.  The  papers 
are  first  attracted  to  the  comb,  but  in 
a  short  time  acquire  some  of  its  electri- 
fication, and  then  are  repelled. 

§  210.  Two  states  of  electri- 
city. —  It  is  quite  apparent  that  we  are  now  dealing  with  a  very 
different  class  of  electrical  phenomena  from  any  that  we  have 
previously  observed.  It  is  also  quite  as  obvious  that  we  are 
dealing  with  electricity  in  a  very  different  state  or  condition 
from  that  in  which  we  have  before  studied  it.  Hitherto  we 
have  studied  only  those  phenomena  produced  by  electricity 


Fig.  175. 


TWO    STATES   OF    ELECTRICITY. 


239 


when  in  motion  ;  and,  inasmuch  as  when  in  that  state  its  energy 
is  expended  in  work,  or  transformed  into  some  other  form  of 
energy  as  rapidly  as  it  is  generated,  there  was  no  such  thing 
as  an  accumulation  of  electricity.  In  our  late  experiments 
there  is  wanting  anything  like  a  current ;  but,  on  the  other  hand, 
we  find  that  electricity  in  this  new  state  may  accumulate,  be 
stored  up,  and  remain  in  a  quiescent  state  for  an  indefinite 
time.  In  the  latter  state  it  is  incapable  of  affecting  a  magnetic 
needle,  magnetizing,  generating  heat,  illuminating,  producing 
decomposition,  or  giving  shocks.  But  in  this  state  of  appar- 
ent repose  it  may  attract  and  afterwards  repel  light  bodies  in 
the  vicinity  of  the  body  in  which  it  resides.  These  attrac- 
tions and  repulsions  are  quite  distinct  from  the  attractions  and 
repulsions  which  occur  between  parallel  currents. 

This  state  of  electricity  is  called  static,  in  distinction  from  the 
current  state,  which  is  often  called  dynamic.  We  have  seen 
that,  under  certain  conditions,  electricity  may  change  from  one 
state  to  the  other,  as  when  the  electricity  which  had  accumu- 
lated in  the  boy  on  the  insulated  stool  passed  to  the  other  boy, 
producing,  in  its  current  Fig  176 

state,  both  illuminating  and 
physiological  effects ;  and 
again,  when  a  current  is 
broken,  the  current  ceases, 
but  electricity  accumulates 
in  the  wire  (see  §  208) .  We 
have  also  learned  that  elec- 
tricity of  high  potential, 
such  as  is  most  readily  de- 
veloped by  friction,  exhib- 
its the  static  phenomena,  i.e.,  attractions  and  repulsions,  most 
strikingly ;  but  we  must  be  careful  to  avoid  the  notion  that 
these  are  peculiar  to  electricity  so  derived. 

§211.  Two  kinds  of  electrification.— Experiment  1.  Bend 
a  small  glass  tube  into  the  form  represented  by  A,  Figure  176,  and  insert 


240 


ELECTRICITY   AND   MAGNETISE  I. 


Fig.  177. 


one  end  in  a  block  of  wood  B  for  a  base ;  and  suspend  from  the  tube  a 
pith-ball  C  by  a  silk  thread.  Rub  a  glass  rod  D  with  a  silk  handker- 
chief, and  present  it  to  the  ball ;  attraction  at  first  occurs,  followed  by 
repulsion  after  contact.  Now  rub  a  stick  of  sealing-wax,  or  a  hard- 
rubber  ruler,  with  flannel,  and  present  it  to  the  ball,  which  is  in  a  con- 
dition such  that  it  is  repelled  by  the  electrified  glass ;  it  is  attracted  by 
the  electrified  sealing-wax.  We  are  led  to  suspect  that  the  sealing- 
wax  possesses  a  different  kind  of  electri- 
fication from  that  of  the  glass.  Let  us 
further  test  the  matter. 

Experiment  2.  Suspend  two  glass 
rods  that  have  each  been  rubbed  with 
silk  in  two  wire  stirrups  (Fig.  177) ,  and 
present  them  to  each  other ;  they  repel 
one  another.  Suspend  two  sticks  of 
sealing-wax  that  have  been  rubbed  with 
flannel  in  the  same  manner;  the  same 
result  follows.  Now,  in  a  like  manner,  present  one  of  the  glass  rods 
and  one  of  the  sticks  of  sealing-wax  to  each  other ;  they  attract  one 
another. 

Experiment  3.  Make  a  pin 
hole  in  each  end  of  a  hen's  egg, 
and  blow  its  liquid  contents  out. 
Apply,  with  flour  paste,  tinfoil 
smoothly  to  the  surface  of  the 
shell,  and  completely  cover  it. 
With  a  drop  of  melted  sealing-wax 
attach  one  end  of  a  silk  thread 
midway  between  the  ends  of  the 
shell,  so  that  it  may  be  suspended, 
as  in  Figure  178.  Repeat  the  last 
two  experiments  with  the  shell  as 
with  the  pith-ball ;  you  obtain  simi- 
lar results. 

It  is  evident  (1)  that  there 
are  two  kinds  or  conditions  of 
electrification;  or,  for  conven- 
ience, we  sometimes  say  two  kinds  of  electricity;  (2)  that  they 
are  so  related  to  each  other  that  like  kinds  repel  and  unlike  kinds 
attract  one  another.  The  two  kinds  are  usually  distinguished 


Fig.  178. 


INDUCTION. 


241 


from  one  another  by  the  names  positive  and  negative,  or,  more 
briefly,  as  -\-e  and  —  e.  The  former  is,  by  definition,  such  as 
is  developed  on  glass  when  rubbed  with  silk,  and  the  latter  is 
the  kind  developed  on  sealing-wax  when  rubbed  with  flannel. 
There  is  no  reason,  except  custom,  for  calling  the  one  positive 
rather  than  the  other. 

Experiment  4.  Once  more  electrify  a  stick  of  sealing-wax  with  a 
flannel,  and  present  it  to  the  ball  or  shell,  and  after  the  ball  is  repelled, 
bring  the  surface  of  the  flannel  which  had  electrified  the  rod  near  the 
ball ;  the  ball  is  attracted  by  it,  showing  that  the  rubber  is  also  electri- 
fied and  with  the  opposite  kind  to  that  which  the  sealing-wax  pos- 
sesses. (Which  kind  of  electrification  has  the  flannel?) 

Fig.  179. 


One  kind  of  electrification  is  never  developed  alone  ;  when  two 
substances  are  rubbed  together,  both  always  become  oppositely 
electrified,  and  to  an  equal  amount.  In  general,  whenever  any 
electricity  of  either  sign  is  developed,  an  equal  quantity  of  the 
other  is  to  be  found.  (Ascertain  the  kind  of  electrification  de- 
veloped on  a  rubber  comb  when  it  is  passed  through  the  hair ; 
also  the  kind  developed  on  a  person  when  whipped  with  fur,  by 
presenting  the  bodies  whose  electrification  is  to  be  tested  to  a 
body  having  a  known  electrification.) 

§  212.  Induction. — Experiment.  Suspend  two  egg-shells,  pre- 
pared as  above,  so  as  to  touch  one  another,  end  to  eud,  as  in  Figure  179. 


242  ELECTRICITY   AND   MAGNETISM. 

Bring  near  to  one  end  of  the  shells,  but  not  to  touch,  a  sealing-wax  rod 
excited  with  flannel,  and  therefore  having  —  e.  While  the  rod  is  in  this 
position,  carry  a  thin  strip  of  tissue  paper,  or  a  pith-ball  suspended  by 
a  silk  thread,  along  the  eggs.  The  paper  is  attracted  most  strongly  at 
the  ends ;  but  in  the  middle,  where  the  shells  are  in  contact,  there  is 
very  little  electrification.  Separate  B  from  A  about  10cm,  while  the  rod 
D  is  still  in  position.  Then  place  D  midway  between  A  and  B ;  the  rod 
repels  B  and  attracts  A.  It  appears  that  when  the  two  shells  touched 
one  another,  thereby  constituting  practically  one  body,  that  the  shells 
were  oppositely  electrified,  as  represented  by  the  signs  +  and  —  in  the 
diagram ;  and  when  the  two  bodies  were  separated,  they  retained  their 
opposite  charges. 

"We  learn  from  this  experiment  that  by  induction  we  may 
charge  at  the  same  time  two  bodies,  one  with  -f-e,  and  the  other 
with  -e. 

§  213.  Discharge. — Experiment.  Bring  the  two  shells  oppo- 
sitely charged  near  one  another;  when  near  enough  they  exhibit 
mutual  attraction  for  one  another.  On  bringing  them  still  nearer,  a 
spark  passes  between  them,  their  mutual  attraction  suddenly  ceases, 
and  on  testing  them  with  an  electroscope,  it  is  found  that  both  have 
lost  their  electrification,  i.e.,  both  have  become  discharged. 

WJien  two  bodies  containing  equal  amounts  of  opposite  electri- 
cities are  brought  together,  both  become  discharged.  During 
the  process  of  discharge,  the  electricity  which  was  previously  in 
a  condition  of  rest,  or  a  static  state,  assumes  a  condition  of 
motion,  or  a  dynamic  state,  as  is  shown  by  a  spark  passing 
between  the  two  bodies  when  brought  near  one  another.  One 
of  the  bodies — that  positively  charged— is  at  a  potential  higher 
than  that  of  the  earth,  the  other  being  lower.  When  they  are 
brought  sufficiently  near,  the  tendency  for  the  electricity  to  pass 
from  the  region  of  higher  potential  becomes  strong  enough  to 
penetrate  the  insulating  air  and  establish  a  condition  of  equili- 
brium. In  this  particular  case  the  result  is  zero  potential  or 
no  electrification  ;  but  in  general  both  bodies  would  be  left  at  a 
like  condition  of  electrification,  its  sign  depending  upon  the 
sign  of  that  electricity  which  was  in  excess. 

We  may  now  understand  how  it  is  that  an  electrified  body 


INSULATION.  243 

attracts  to  itself  light  bodies  in  its  vicinity.  For  example,  a 
stick  of  sealing-wax,  excited  with  —  e,  brought  near  a  pith  ball, 
induces  -\-e  next  itself,  and  repels  —  e  to  its  farthest  side ;  then, 
of  course,  attraction  follows.  There  is  the  same  attraction  be- 
tween heavy  bodies,  but  usually  not  sufficient  to  produce  motion. 

§  214.  Insulation. — Experiment.  Bring  again  the  electrified  seal- 
ing-wax near  one  end  of  one  of  the  shells ;  the  shell  becomes  polarized, 
that  is,  the  opposite  ends  become  oppositely  electrified.  Touch  the  shell 
with  the  finger.  Through  your  body  the  negative  charge  is  driven  to 
the  earth,  while  the  positive  charge  remains  in  proximity  to  the  rod. 
(Explain.)  Remove  the  finger,  and  afterwards  remove  the  rod;  test 
the  shell,  and  you  will  find  that  it  is  charged  with  electricity.  (Is  it 
— e  or  +e?)  Touch  this  shell  with  the  other  shell,  then  separate  them. 
Test  them,  and  you  find  that  they  have  the  same  kind  of  electrification. 
It  is  evident  that  the  first  shell  became  electrified  by  induction  and  the 
last  shell  by  conduction.  Touch  with  the  finger  one  of  the  shells ;  it 
loses  its  electrification. 

When  you  touch  the  shell  with  your  finger,  the  electric  charge 
diffuses  itself  through  your  body  and  the  earth.  It  is  evident 
that  the  electricity  could  not  traverse  the  silk  thread,  otherwise 
we  could  not  have  charged  the  shell.  Substances  which  do  not 
allow  electricity  to  pass  readily  through  them  are  called  non- 
conductors or  insulators.  A  body  that  is  to  receive  a  permanent 
charge  of  electricity  must  be  insulated,  i.e.,  have  no  connection 
with  the  earth  through  a  conducting  substance.  Some  of  the 
best  insulating  substances  are  dry  air,  ebonite,  shellac,  resins, 
glass  (free  from  lead,  e.g.,  common  bottle  glass),  silks,  and 
furs.  In  experiments  with  electricity  in  the  statical  state,  the 
E.  M.  F.  is  in  general  so  much  greater  than  when  a  galvanic 
battery  is  the  source  of  electricity,  that  substances  —  such  as  dry 
wood,  for  instance  —  which  are  practically  good  insulators  in  the 
latter  case  are  not  so  regarded  in  the  former.  Moisture  injures 
the  insulation  of  bodies ;  hence  experiments  succeed  best  on 
dry,  cold  days  of  winter,  when  moisture  of  the  air  is  least  liable 
to  be  condensed  on  the  surfaces  of  apparatus,  especially  if  it  is 
kept  warm. 


244  ELECTRICITY   AND   MAGNETISM. 

§  215.  Electrification  confined  to  the  external  surface. 
—  Experiment  1.  Place  a  tin  fruit-can  on  a  clean,  dry  glass  tumbler 
(Fig.  180).  Fasten  a  circular  disk  a  of  tin  15mm  in  diameter  to  owe  end 
of  a  rod  of  sealiug-wax.  Charge  the  can  heavily  with  electricity  from 
an  electrical  machine  (seep.  245).  Through  an  orifice  c  in  the  can 
introduce  the  disk,  and  touch  the  interior  surface  of  the 

lou. 

can.  Withdraw  the  disk,  and  present  it  to  an  electroscope. 
It  shows  no  electrification.  Now  touch  the  exterior  sur- 
face of  the  can  with  the  disk,  and  present  it  to  the  electro- 
scope ;  it  is  found  to  be  electrified. 

Experiment  2.  Attach  to  the  can  a  gold  foil,  or  double 
pith-ball  electroscope,  and  put  into  the  can  a  few  feet  of 
metal  chain.  Fasten  the  outer  end  to  a  rod  of  glass,  or 
some  other  insulator,  and  charge  the  can  till  the  leaves  of  the  electro- 
scope diverge  widely.  Then  draw  up  the  chain  by  the  glass  rod ;  the 
leaves  come  together  somewhat.  Drop  the  chain  into  the  can;  the 
leaves  separate  again,  showing  that  the  charge  had  not  been  lost. 

These  experiments  show  (1)  that  no  electricity  can  be  found 
inside  of  a  hollow-charged  body ;  or,  roughly  stated,  electricity 
at  rest  resides  on  the  exterior  surfaces  of  bodies;  (2)  that 
ivhen  the  exterior  surface  of  an  electrified  body  is  increased  with- 
out increasing  its  mass  or  the  charge,  the  amount  of  electricity  at 
any  point  is  diminished. 

§  216.  Electrical  potential.  — We  have  seen  that  the 
passage  of  electricity  from  point  to  point  sometimes  causes  a 
spark ;  so,  conversely,  the  spark  indicates  the  passage  of  elec- 
tricity. The  passage  of  a  current  from  one  shell  to  the  other 
(Fig.  179)  might  be  proved,  and  its  direction  determined,  by 
connecting  the  shells  by  wires  joined  to  a  suitable  galvanome- 
ter. The  current  would  flow  from  A  charged  with  -f  e,  to  B 
charged  with  —e,  thus  showing  that  A  had  a  higher  potential 
than  B.  A  body  charged  with  +e  is  understood  to  be  one  that 
has  a  higher  potential  than  that  of  the  earth,  and  a  body 
charged  with  —  e  is  one  that  has  a  lower  potential  than  that 
of  the  earth,  the  potential  of  the  earth  being  regarded  for  con- 
venience as  zero. 


PLATE   MACHINE. 


245 


With  a  very  sensitive  electroscope  it  can  be  shown  that  the 
wires  connected  with  the  plates  of  a  galvanic  battery  are  at 
different  potentials  when  the  circuit  is  broken.  But  the  differ- 
ence of  potential  is  so  small,  compared  with  the  difference  pro- 
duced by  friction,  that  a  thousand  gravity  cells  in  series  give 
a  spark  only  about  -f^  of  an  inch  long , 


XXXV.     ELECTRICAL  MACHINES.  —  CONDENSERS,  ETC. 

§  217.  If,  then,  for  any  purpose  we  wish  electricity  of  high 
potential,  we  must  use  an  enormous  number  of  cells,  an  induc- 
tion coil,  or,  more  cheaply  and  conveniently,  an  electrical 
machine  depending  either  on  friction  or  on  the  induction  of  a 
charge  of  electricity.  Brief  descriptions  of  a  few  machines  will 
now  be  given,  followed  by  a  series  of  experiments  that  may  be 
performed  with  them. 

Fig.  181. 


§  218.  Plate  machine.  —  It  consists  of  a  positive  or  prime 
conductor  A,  a  negative  conductor  B,  a  glass  plate  C,  a  rubber  D, 
made  of  two  cushions  of  leather  covered  with  an  amalgam,  four  insu- 
lating supports  E,  F,  G,  and  H,  a  silk  insulating  bag  I,  and  a  brass 
chain  K,  used  to  connect  either  conductor  with  the  earth.  An  exten- 
sion of  the  prime  conductor  L  consists  of  two  combs,  one  on  either 
side  of  the  plate ;  their  pointed  teeth  are  turned  toward  the  plate.  M  is 
a  pith-ball  electroscope. 


246 


ELECTRICITY   AND   MAGNETISM. 


Fig.  182. 


When  the  plate  is  turned  in  the  direction  indicated  by  the 
arrow,  it  passes  between  the  rubbers,  and  the  friction  generates 
4-  e  on  the  plate  and  —  e  on  the  rubber.  The  electrified  portion 
of  the  plate  then  passing  through  the  silk  bag  comes  opposite 
the  comb,  when  it  polarizes  the  prime  conductor,  attracting  —  e 
and  repelling  -\-e.  But  the  —  e  escapes  from  the  points  of  the 
comb  (see  §  226)  to  the  plate  and  neutralizes  the  +e  of  the  plate, 
and  thereby  leaves  the  conductor  charged  with  -f-e.  If  both  con- 
ductors are  insulated  at  the  same  time,  the  mutual  attraction  of 
the  two  kinds  of  electricity  would  prevent  their  becoming  heavily 

charged,  so  one  of  the  con- 
ductors is  always  connected  to 
earth  by  a  chain.  If  -j-e  is 
wanted,  A  is  insulated  ;  if  —  e 
is  wanted,  B  is  insulated. 

§  219.  Blectrophorus.  -, 
Experiment.  On  a  circular  dislt 
of  sheet-iron  or  tin  26cm  in  diame- 
ter cement  a  circular  disk  of  vul- 
canite 22cm  in  diameter.  To  the 
center  of  another  circu- 
lar disk  of  tin  18cm  in 
diameter  (Fig.  182)  ap- 
ply with  heat  one  end  of 
a  stick  of  sealing-wax 
for  a  handle.  Strike  the 
surface  of  the  vulcanite 
a  few  times  with  a  cat's 
fur  or  a  fox-tail ;  it  will 
become  electrified  with 
— e.  Then  place  the  tin 
disk  on  the  vulcanite ; 
— e  of  the  vulcanite  will 
polarize  the  disk,  induc- 
ing +e  on  its  lower  sur- 
face and  —  e  on  its  upper  surface.  Now  place  a  finger  on  the  disk.  The 
—e  will  escape  through  your  body  to  the  earth,  but  the  -\-e  will  remain 


CONTINUOUS  ELECTROPHORUS.          247 

on  the  disk,  bound  by  the  —  e  of  the  vulcanite.  Finally,  raise  the  disk 
by  its  insulating  handle.  Kemoved  from  the  influence  of  the  —  e  on  the 
vulcanite,  the  -{-e  of  the  disk  is  now  free,  and  if  a  knuckle  of  one  of 
your  hands  (Fig.  183)  is  brought  near  it,  a  bright  spark  will  pass  from 
it  to  your  hand,  and  it  will  become  discharged. 

The  disk  may  be  charged  and  discharged  in  the  same  manner  a  great 
number  of  times  without  again  whipping  the  vulcanite  with  the  fur. 
A  Leydeii  jar  (page  250)  may  be  charged  with  this  apparatus  in  a  few 
minutes.  (Is  the  disk  charged  by  conduction  or  induction?  What  are 
the  proofs?) 

§  220.  Continuous  electrophorus.  —  Various  methods 
have  been  adopted  for  developing  electricity  continuously  from 
the  electrophorus,  and  more  Fig.  184. 

rapidly  and  with  less  manipu- 
lation than  can  be  done  with 
the  apparatus  above  described. 
Figure  184,  from  which  the 
supporting  parts  are  omitted 
for  the  sake  of  simplicity,  will 
serve  to  illustrate  the  general 
principle  of  such  machines. 

A  is  a  vulcanite  or  glass 
wheel,  which  can  be  rotated  by  means  of  a  system  of  wheels 
CC.  About  2cm  back  of  A  is  a  vulcanite  sector  D,  which  serves 
as  an  inducer,  or  the  same  purpose  as  the  vulcanite  disk  of  the 
electrophorus.  Opposite  D  and  in  front  of  A  is  a  metallic  comb 
B,  which  is  connected  with  the  conductor  N.  Let  —  e  be  ex- 
cited on  D  with  a  cat-skin.  Then  the  conducting  system  NB 
will  be  polarized  by  its  influence ;  —  e  will  be  driven  to  its 
farthest  extremity  N,  and  -\-e  drawn  to  the  points  of  the  comb 
B.  Then,  since  electricity  escapes  readily  from  points,  the 
-\-e  will  leap  from  B  to  A,  drawn  off  from  the  points  by  the 
—  e  of  D.  But  vulcanite  being  a  non-conductor,  only  that 
portion  of  the  surface  of  A  will  be  charged  with  -\-e  that  is 
directly  opposite  the  comb  B.  The  conductor  BN,  being  de- 
prived of  its  +e,  is  left  charged  with  free  —e.  Now,  rotate  the 


248 


ELECTRICITY   AND   MAGNETISM. 


disk  A.  When  it  has  accomplished  half  a  revolution,  that  por- 
tion of  it  which  is  charged  with  -\-e  comes  opposite  another 
comb  B',  which  is  also  connected  with  a  conductor  P.  The  con- 
ductor B'P  becomes  polarized.  Its  —e  passes  off  from  the 
points  of  B'  to  the  disk  A,  and  discharges  the  +6  on  this  disk, 
while  the  conductor  PB'  is  left  charged  with  free  +e.  It  is 
evident  that  a  constant  rotation  of  A  would  cause  it  to  be  con- 
stantly charged  with  -\-e  at  its  lower  part  by  the  influence  of  the 
sector  D,  and  constantly  discharged  at  its  upper  part,  while  the 
conductor  BN  is  constantly  receiving  a  charge  of  —  e  in  conse- 
quence of  the  loss  of  its  -f-e  ;  and  for  a  similar  reason  the  con- 
ductor B'P  is  con- 
Fig.  185.  ,  i  .  . 

stantly  receiving  a 
charge  of  +e.  With 
a  rapid  rotation  of 
the  disk  the  two  con- 
ductors will  be  so 
rapidly  and  highly 
electrified,  the  one 
with— e  and  the  other 
with  +e,  that  under 
the  influence  of  their 
mutual  attraction  al- 
most an  incessant  flow 
of  sparks  will  pass 
between  them,  even 
when  the  extremities, 
P  and  N,  are  several 
inches  apart. 

§  221.  Carre  ma- 
chine. —  The  sector  D  is  liable  to  lose  its  charge  suddenly, 
and  loses  it  very  quickly  after  the  operation  of  the  machine 
ceases  ;  so  that,  to  begin  again,  it  is  necessary  to  recharge  the 
sector.  In  the  Carre"  machine  this  difficulty  is  avoided. 


CONDENSER.  249 

A  circular  plate  of  glass  A,  which  serves  as  the  inducer,  passes 
between  two  leather  cushions  B,  as  it  is  rotated  by  means  of  the  crank 
C ;  and  thus  by  friction,  occasioned  by  rubbing  against  the  cushions,  the 
plate  is  kept  constantly  and  highly  electrified  during  the  operation  of 
the  machine.  By  means  of  a  system  of  pulleys,  motion  is  communi- 
cated from  the  shaft  of  the  plate  A  to  the  shaft  of  an  ebonite  disk  D. 
The  glass  plate  A  becomes  electrified  with  +e.  The  method  by  which  the 
plate  D  and  the  conductors  F  and  E  become  charged  is  like  that  of  the 
machine  last  described.  (Explain.)  The  cylinder  E,  called  the  prime 
conductor,  has  a  large  area,  and  is  therefore  capable  of  receiving  a 
large  charge.  The  conductor  F  is  so  jointed  at  N  that  it  may  be  brought 
near  or  carried  away  from  E.  During  operation  the  conductor  F  should 
be  connected  by  a  chain,  or  other  good  conductor,  with  the  earth. 
When  in  operation,  if  F  is  brought  within  two  or  three  inches  of  E, 
sparks  will  pass  between  them  so  rapidly  as  to  present  the  appearance 
of  a  constant  and  continuous  line  of  light.  If  F  is  removed  to  quite  a 
distance  from  E,  the  charge  will  so  accumulate  in  E  that  sparks  five 
or  six  inches  in  length  may  be  drawn  from  it  with  the  fist.  If  a 
Leyden  jar  (§  223)  is  suspended  by  its  knob  from  the  loop  G,  and  its 
outside  coating  connected  with  F,  the  discharge  will  become  so  intense 
as  to  produce  a  report  nearly  as  loud  as  that  of  a  pistol. 

§  222.  Condenser.  —  A  very  important  adjunct  to  an  elec- 
trical machine  is  a  condenser  of  some  kind,  by  means  of  which 
a  large  quantity  can  be  collected  on  a  small  surface. 

Experiment.  Let  a  person  stand  on  an  insulated  stool  (p.  237) ,  and 
place  one  hand  on  the  prime  conductor  of  a  machine.  Let  the  other 
open  hand  press  against  a  plate  of  glass  or  disk  of  vulcanite,  held  on  the 
open  hand  of  a  second  person  standing  on  the  floor.  After  a  few  turns 
of  the  machine,  let  the  hand  that  has  been  on  the  prime  conductor 
grasp  the  free  hand  of  the  second  person.  Quite  a  shock  will  be  felt 
by  both.  Or  the  connection  may  be  made  through  a  group  of  persons 
having  hold  of  one  another's  hands,  when  the  whole  company  may 
receive  a  shock. 

It  is  evident  that  by  this  process  an  unusual  quantity  of  elec- 
tricity had  collected  previous  to  the  discharge.  The  explanation 
is  simple.  The  hand  of  the  first  person,  charged  with  -f  e,  acts 
by  induction  through  the  glass  upon  the  second  person,  attract- 
ing — e  to  the  surface  of  the  glass  with  which  his  hand  is  in 


250  ELECTRICITY  AND   MAGNETISM. 

contact,  and  repelling  -fe  to  the  earth.  Thus,  through  their 
mutual  attraction,  the  two  kinds  of  electricity  become,  as  it- 
were,  heaped  up  opposite  each  other,  and  yet  are  prevented,  by 
the  insulating  glass,  from  uniting. 

§  223.   Leyden  jar.  —  The  most  convenient  form  of  con- 
Fig  186       denser  is  the  Leyden  jar.     Coat  a  green  glass  quart 
fruit-jar  (Fig.  186),  within  and  without,  for  about 
two-thirds  its  hight,  with  tin  foil,  using  flour  paste. 
Close  the   mouth  with   a   cork   saturated    with  hot 
paraffine.     Through  the  cork  pass  a  stout  brass  wire 
till  it  touches  the  inner  foil.     Cast  a  lead  bullet  a  on 
the  exposed  end  of  the  wire.     Clean,  warm,  and  var- 
nish the  exposed  glass  surface  of  the  jar,  and  when  thoroughly 
dry  it  is  ready  for  use. 

The  jar  may  be  charged  by  connecting  one  of  its  coatings 
with  the  -f  conductor,  and  the  other  with  the  —conductor  of  an 
electrical  machine,  or  by  connecting  one  of  the  coatings  with 
Fig.  is?.  one  of  the  conductors,  and  the  other  with 

the  earth.  Or  it  may  be  charged  by  con- 
necting the  outside  coating  with  one  of  the 
poles  of  the  secondary  coil  of  an  induction 
coil,  and  bringing  the  other  pole  near  to  the 
ball  leading  from  the  fnner  coating.  To 
discharge  the  jar,  connect  the  outer  coating 
with  the  knob  of  the  jar.  To  avoid  a  shock  in  so  doing,  prepare 
a  discharger  as  follows:  Through  the  cork  of  a  bottle  (e.g.,  a 
soda-water  bottle,  Figure  187)  pass  a  stout  brass  semicircular 
wire.  Cast  on  each  of  its  ends  a  lead  bullet.  Use  the  bottle 
as  an  insulating  handle. 

The  effects  are  greater  in  proportion  to  the  number  and  size 
of  the  jars  in  electrical  connection.  Let  any  number  of  jars 
(Fig.  188)  be  placed  on  a  sheet  of  tin  foil,  by  which  their 
outer  coatings  are  connected.  Connect  also  their  inner  coat- 
ings with  one  another  by  a  wire  running  around  their  projecting 


ELECTRICITY   NOT   IN   THE   COATINGS. 


251 


rods.  The  several  jars  are  by  this  means  practically  converted 
into  one  large  jar.  This  combination  of  jars  is  called  a  Leyden 
battery.  A  strip  of  gold  leaf  placed  on  the  glass  slip  a  may 
be  fused,  and  even  volatilized,  by  a  battery  discharge  passed 
through  it ;  cards  and  slips  of  glass  may  be  perforated,  and 
gas  or  ether  ignited. 

§  224.  Electricity  not  in  the  coatings.— If  the  two  per- 
sons in  the  experiment  (p.  249)  both  remove  their  hands  from 
the  glass  plate,  after  they  have  been  charged,  and  grasp  one 
another's  hands,  they  experience  little  or  no  shock.  But  if  they 


Fig.  188. 


replace  their  hands  on  the  glass,  and  grasp  one  another's  hands, 
they  receive  a  shock.  This  shows  that  electricity  was  not  on 
their  bodies,  but  on  the  surface  of  the  glass.  The  coatings  of  a 
Leyden  jar  serve  the  purpose  of  conductors  to  spread  electricity 
on  the  glass  at  the  time  of  charging,  and  to  allow  its  escape 
from  all  parts  of  its  electrified  surface  at  the  time  of  a  discharge. 

QUESTIONS. 

1.  An  insulated  jar  cannot  receive  a  great  charge.    Why? 

2.  If  points  are  attached  to  the  outer  coating  of  an  insulated  jar,  it 
can  receive  a  much  larger  charge.    Why? 


252  ELECTRICITY  AND   MAGNETISM. 

3.  If  the  knob  of  a  second  jar  be  held  near  the  outer  coating  of  an 
insulated  jar,  sparks  will  pass  from  the  coating  to  the  knob,  and  both 
jars  will  be  charged.  Suppose  that  the  inner  coating  of  the  first  jar  is 
charged  with  +e,  what  kind  of  electricity  will  each  of  the  other  coat- 
ings have? 

§  225.  Attractions  and  repulsions.  —Experiment  1.  Sup- 
port a  plate  of  window  glass  (Fig.  189)  about  5cm  from  a  table.  Rub  its 

upper  surface  with  a  silk  handkerchief, 
and  place  pith-balls,  or  bits  of  tissue  paper, 


on  the  table  beneath  the  glass.     They  will 
dance  up  and  down  between  the  plate  and 
table  in  a  lively  manner.     (Explain.) 
Experiment  2.  Place  a  handful  of  bits  of  tissue  paper  on  a  tin  disk 
supported  by  a  prime  conductor  of  an  electrical  machine.     The  papers 
become  excited,  are  repelled  into  the  air,  and  fall  on  all  sides,  giving 
the  appearance  of  a  miniature  snow-storm. 

Experiment  3.  Apply  one  end  of  a  discharger  to  the  conductor  of 
a  machine,  and  the  other  end  to  the  inner  surface  of  a  glass  tumbler, 
and  charge  the  interior  with  electricity,  and  then  place  it  over  some 
pith-balls,  or  images  cut  from  pith;  a  ludicrous  dance  will  be  kept  up 
for  several  minutes. 

The  electric  whirl  consists  of  a  cap  of  metal  resting  upon  a 
pointed  wire,  which  serves  as  a  pivot.     The  cap  has  pointed 
wires  branching  out  from  it,  like  the  spokes  of  a 
wheel,  and  bent  near  their  ends  at  right  angles, 


and  all  turned  in  the  same  direction,  as  shown  in 
Figure  190.  When  this  apparatus  is  placed  upon 
the  conductor  of  a  machine,  the  air  particles 
around  the  highly  electrified  points  become  ex- 
cited, and  are  repelled,  producing  a  current  of  air 
issuing  from  the  points.  The  reaction  causes 
the  wheel  to  revolve  in  the  opposite  direction,  as  indicated  by 
the  arrows  in  the  figure.  A  candle  flame  placed  near  the  point 
of  a  rod  attached  to  a  conductor  will  be  extinguished. 

§  226.  Effect  of  points.  —  We  might  reasonably  expect 
that  a  current  of  excited  air-particles  issuing  from  points  on 
an  excited  conductor  would  serve  to  carry  away  with  them  elec- 


LUMINOUS   EFFECTS. 


253 


Fig.  191. 


tricity  from  the  conductor  ;  in  other  words,  to  discharge  it.    Do 
they  produce  this  result? 

Experiment.  While  the  electrical  machine  is  in  operation,  hold 
your  knuckle  near  the  conductor;  a  succession  of  sparks  will  pass 
from  the  conductor  to  your  hand.  Now  place  several  points  on  the 
conductor,  and  again  present  your  knuckle  as  before ;  either  no  sparks 
will  pass  to  your  knuckle,  or,  at  most,  very  feeble  ones,  and  in  a  few 
seconds  after  the  operation  of  gener- 
ating electricity  ceases,  the  conductor 
will  be  found  completely  discharged, 
although  it  Is  thoroughly  insulated.  It 
is  apparent  that  the  electricity  escaped 
from  the  points. 

We  conclude,  therefore,  that  the 
effect  of  points  on  an  electrified  in- 
sulated body  is  greatly  to  facilitate 
the  discharge  of  its  electricity. 

§  227.  Luminous  effects.  — 
Figure  191  represents  a  glass  shade 
having  circular  bits  of  tinfoil  pasted 
spirally  around  it,  from  top  to  bot- 
tom, and  about  lmm  apart.  If  the 
poles  of  an  induction  coil,  or  the 
conductors  of  an  electrical  machine,  are  connected,  one  with 
each  extremity  of  this  spiral  line,  an  intermittent  line  of  light 
will  be  produced  in  the  path  of  the  current  by  the  sparks  which 
appear  at  the  intervals  between  the  bits  of  foil.  All  experiments 
illustrating  luminous  effects  should  be  performed  in  a  dark  room. 

Beautiful  luminous  effects  may  be  produced  with  apparatus 
arranged  as  follows :  Apply  to  one  surface  of  a  mica  disk  (Fig. 
192),  about  15  x  10cm,  a  sheet  of  silver  leaf  or  tin  foil,  8  x  5cm. 
Place  two  pointed  poles  of  an  inductorium,  or  a  Carre"  machine, 
within  lcm  of  the  foil,  and  as  far  apart  as  the  power  of  the 
machine  will  admit.  Sparks  will  leap  from  the  poles  to  the  foil, 
and  travel  in  tortuous  branching  lines  between  the  poles. 


254  ELECTRICITY   AND   MAGNETISM. 

If  air  is  partially  exhausted  from  the  glass  tube  used  in  illus- 
trating the  law  of  falling  bodies  (Fig.  87,  page  106),  and  the 
poles  of  a  coil  or  machine  are  applied  to  the  opposite  extremi- 
ties of  the  tube,  sparks  of  electricity  passing  through  the  rarefied 
air  spread  out  in  sheets  of  bluish  white  light  resembling  the 
auroral  lights,  hence  this  tube  has  received  the  name  Aurora 
tube. 

Fig.  192. 


If  a  circular  disk  is  divided  into  black  and  white  sectors,  as 
In  Figure  193,  and  rotated  very  rapidly  in  ordinary  daylight, 
the  colors  blend,  and  the  disk  appears  of  a  uniform  gray  color. 
Fi«.  193.  But  if   the  disk  is   illuminated  in  a 

darkened  room  by  the  electric  spark, 
each  sector  appears  separate,  and  the 
disk  appears  to  be  at  rest.  A  rail- 
road train  in  rapid  motion,  and  even 
its  wheels,  appear  to  be  at  rest  when 
illuminated  on  a  dark  night  by  a  flash 
of  lightning.  This  shows  that  the 
duration  of  an  electric  spark  must  be 
very  brief,  inasmuch  as  it  fails  to 
illuminate  these  objects  in  two  successive  positions. 

The  remarkable  beauty  and  brilliancy  of  the  discharge  is 
perhaps  best  exhibited  by  means  of  the  well  known  Geissler's 
tubes.  These  tubes  contain  highly  rarefied  vapors  and  gases  of 
various  kinds.  Platinum  wires  are  sealed  into  the  glass  at  each 
end  to  conduct  the  electric  current  through  the  glass.  The 
light,  instead  of  appearing,  as  in  the  Aurora  tube,  like  a  stream 


LIGHTNING.  255 

pouring  from  pole  to  pole,  is  often  striated  or  divided  trans- 
versely into  luminous  sections,  with  alternating  darker  sections, 
as  shown  in  Figure  194.  These  striae  vary  in  shape  and  color 

Fig.  194. 


with  the  degree  of  the  vacuum,  and  the  kind  of  gas  or  vapor 
through  which  the  discharge  passes.  Experiments  with  these 
tubes  succeed  best  when  used  with  the  induction  coil. 

§  228.  Lightning.  —  Certain  clouds  which  have  formed  very 
rapidly  are  highly  charged  with  electricity,  usually  positively 
charged.  The  surface  of  the  earth  and  objects  thereon  imme- 
diately beneath  the  cloud  are  charged  inductively  with  the 
opposite  kind  of  electricity.  The  cloud  and  the  earth  corre- 
spond to  the  coatings,  and  the  intervening  air  to  the  glass  of  a 
huge  Leyden  jar.  The  charge  in  the  earth  and  that  in  the  cloud 
hold  one  another  prisoner  by  their  mutual  attraction,  until,  as 
the  charges  accumulate,  the  attraction  becomes  great  enough  to 
overcome  the  resistance  of  the  intervening  air,  when  a  discharge 
takes  place.  It  is  the  accumulation  of  induced  electricity  on 
elevated  objects,  such  as  buildings  and  trees,  that  offers  an 
attraction  for  the  opposite  electricity  of  the  cloud,  and  renders 
them  especially  liable  to  be  struck  by  lightning. 

§  229.  Lightning-rods.  — The  flash  will  pass  along  the  line 
of  least  resistance.  A  good  lightning  conductor  offers  a  peace- 
ful means  of  communication  between  the  earth  and  a  cloud  ;  it 
leads  the  electricity  of  the  earth  gently  up  toward  the  cloud, 
and  allows  it  to  combine  with  its  opposite  without  disturbance. 


256  ELECTRICITY  AND  MAGNETISM. 

thereby  so  far  discharging  the  cloud  as  to  prevent  a  lightning 
stroke  ;  or,  if  the  tension  is  too  great  to  be  thus  quietly  disposed 
of,  the  flash  strikes  downward,  and  is  led  harmlessly  to  the 
earth  by  the  conductor.  An  ill -constructed  lightning-rod  may 
be  worse  than  none.  A  good  rod  should  be  made  of  good  con- 
ducting material,  so  large  that  it  will  not  be  melted,  and  free 
from  loose  joints.  The  lower  end  should  be  buried  in  earth 
that  is  alwa}rs  moist,  and  the  upper  end  should  terminate  in 
several  sharp  points. 

§  230.  General  observations.  —  Although  the  E.  M.  F. 
of  the  frictional  machine  is  enormous,  still,  the  current  which 
it  can  produce  is  always  small  on  account  of  its  very  great 
internal  resistance.  That  this  resistance  must  be  almost  im- 
measurably greater  than  that  of  any  galvanic  battery  is  evident 
when  we  consider  that  a  part  of  the  circuit  is  always  through 
the  air,  for  instance  in  the  plate  machine,  that  part  between 
the  plate  and  the  comb.  Any  source  of  electricity  that  cannot 
yield  a  strong  current  is,  ordinarily,  of  little  value,  inasmuch  as 
the  amount  of  work  that  can  be  done  by  electricity  is  propor- 
tional to  the  square  of  the  strength  of  the  current.  The  fric- 
tional machine  is,  therefore,  of  little  practical  value,  except  as 
a  source  of  amusement,  and  a  convenient  means  of  investiga- 
ting a  certain  class  of  electrical  phenomena. 

By  an  ingenious  application  of  the  principle  illustrated  by  the 
disk  of  black  and  white  sectors  (Fig.  193),  it  has  been  ascer- 
tained that  the  duration  of  the  spark  is  often  times  less  than 
the  millionth  part  of  a  second,  and  the  velocity  of  the  electric 
discharge  from  a  Ley  den  jar  through  a  short,  thick  copper  wire 
is  280,000  miles  in  a  second. 

The  phenomena  of  electricity  in  a  statical  state  are  limited 
to  those  of  attractions  and  repulsions.  Heating,  luminous, 
magnetic,  physiological,  chemical,  and  mechanical  effects  can  be 
produced  by  electricity  in  the  dynamical  state  only.  In  the 
former  state  it  seeks  the  surface ;  in  the  latter  it  travels 


TRANSFORMATION   OF  ENERGY.  257 

through   the    body.      Statical   and    dynamical  phenomena    are 
rarely  coexistent.     One  must  cease  before  the  other  begins. 

Much  is  known  of  electricity,  its  nature,  its  laws,  and  its 
capacity  for  work  ;  much  remains  to  be  learned.  The  question, 
Wliat  is  electricity?  is  so  far  unanswered.  But  we  may  reason 
as  follows  concerning  it,  and  the  conclusion  answers  all  practi- 
cal purposes.  For  example,  the  energy  of  the  chemical  combi- 
nation of  coal  and  oxygen  in  the  furnace  is  transformed  into 
heat,  heat  works  an  engine,  the  engine  rotates  a  coil  of  wire  in  a 
magnetic  field,  the  motion  of  this  coil  in  the  vicinity  of  a  magnet 
induces  currents  of  electricity  in  the  wire,  these  currents  pro- 
duce an  arc,  and  thereby  heat  and  light.  So  the  energy  of  the 
coal  is  transformed  into  heat  and  light,  through  the  intermediate 
agency  of  electricity.  Hence,  it  is  certain  that  this  intermediate 
agency,  this  so-called  electricity r,  whatever  it  is,  may  receive  and 
impart  energy. 

§  231.  Transformation  of  energy.  —  We  have  found  that 
every  contrivance  for  the  development  of  electric  energy  is  simply 
a  machine  for  the  transformation  of  some  other  form  of  energy 
into  electric  energy.  In  the  voltaic  battery  the  chemical  poten- 
tial energy  of  the  combustibles  is  transformed  into  the  kinetic 
energy  of  the  electric  current.  With  the  magneto  and  frictional 
machines,  mechanical  energy  is  transformed  into  electric  energy. 
In  the  thermopile,  heat  is  changed  directly,  into  electric  energy. 
By  means  of  an  induction  coil,  a  strong  current  of  small  E.M.F. 
is  transformed  into  a  momentary  weak  current  of  great  E.M.F. 
The  kinetic  or  current  form  of  electricity  may,  under  suitable 
conditions,  be  converted  into  the  potential  or  static  state,  and 
vice  versa.  Not  only  are  these  various  forms  of  energy  trans- 
formable into  electric  energy,  but  electric  energy  ma}^  be  changed 
into  any  one. of  these.  Thus  electric  energy  may  be  transformed 
into  heat,  magnetism,  light,  chemical  action,  and  mechanical 
motion.  These  forms  of  energy  are  all  interchangeable  ;  as  in 
fact,  all  known  forms  of  energy  are  mutually  convertible. 


258  ELECTRICITY   AND   MAGNETISM. 

EXERCISES. 

1.  A  spark  of  fire  applied  to  a  mass  of  soap  bubbles,  filled  with  a 
mixture  of  oxygen  and  hydrogen  gases  generated  by  a  galvanic  current, 
produces  a  powerful  explosion.     Commencing  with  the  battery,  state 
the  transformations  of  energy,  in  order,  to  the  final  result. 

2.  The  needle  of  a  galvanometer  connected  with  a  thermopile  is 
deflected.     Trace  the  transformations  of  energy  concerned. 

3.  A  steam  engine  and  a  dynamo  machine  furnish  an  electric  light. 
State  all  the  transformations  of  energy  necessary. 


XXXVI.     USEFUL   APPLICATIONS    OF   ELECTRICITY. 

§  232.  Medical  and  surgical  operations.  —Currents  from 
an  induction  coil  have  great  E.M.F.,  like  f fictional  electricity, 
and  so  can  pass  through  the  poorly  conducting  tissues  of  the 
human  body  and  produce  violent  muscular  contractions.  Cur- 
rents induced  by  a  single  voltaic  cell,  through  the  mediation  of 
an  induction  coil,  may  produce  agonizing  convulsions.  A  vol- 
taic current  has  a  similar  effect  at  the  instants  of  making  and 
breaking  the  circuit  (why  ?) ;  but  b}r  beginning  with  a  mild  cur- 
rent, and  slowly  and  gradually  increasing  its  strength,  a  current 
from  two  hundred  cells  has  been  passed  through  a  person  with 
impunity.  (Explain.)  The  physiological  effect  produced  by  an 
induced  current  at  its  negative  pole  is  more  violent  than  at  the 
positive  pole.  In  this  way  we  may  readily  distinguish  one  pole 
from  the  other  by  simpty  holding  one  in  each  hand.  The  grad- 
ual current  produces  a  benumbing  influence,  or  insensibility  to 
pain.  A  to-and-fro  motion  of  the  current  produces  a  muscular 
agitation  of  the  part  through  which  it  is  sent,  the  tonic  and 
stimulating  effects  of  which  are  similar  to  those  of  muscular 
exercise.  The  galvanic  current  also  exerts  a  powerful  elec- 
trolytic effect  on  the  system.  On  this  principle  it  has  been 
successfully  employed  in.  reducing  tumors,  etc. 

A  platinum  wire  heated  b}r  a  galvanic  current  is  used  like  a 
knife  in  surgical  operations.  The  former  has  the  advantage 


ELECTRIC   LIGHT.  259 

over  the  latter  in  that  it  sears  the  extremities  of  the  blood  ves- 
sels and  thereby  prevents  hemorrhage.  Enough  has  been  said 
to  show  that  a  medical  practitioner  who  can  apply  the  laws  of 
electricity  has  at  his  command  a  powerful  therapeutic  agent; 
but  except  in  experienced  hands  it  is  likely  to  prove  useless,  if 
not  positively  dangerous. 

§  233.  Electric  light.  —  If  the  terminals  of  wires  from  a 
powerful  magneto  machine  or  galvanic  battery  are  brought  to- 
gether, and  then  separated  1  or  2  millimeters,  the  current  does 
not  cease  to  flow,  but  volatilizes  a  portion  of  the  terminals. 
The  vapor  formed  becomes  a  conductor  of  high  resistance,  and 
remaining  at  a  very  high  temperature  produces  intense  light. 
The  light  rivals  that  of  the  sun  both  in  intensity  and  purity. 
The  heat  is  so  great  that  it  fuses  the  most  refractory  substances, 
including  even  the  diamond.  Metal  terminals  quickly  melt  and 
drop  off  like  tallow,  and  thereby  become  so  far  separated  that 
the  electro-motive  force  is  no  longer  sufficient  for  the  increased 
resistance,  and  the  light  is  extinguished.  Hence,  pencils  of 
carbon  (prepared  from 

i         i  -A.    i    •       ^  Fig.  195. 

coke  deposited  in  the  ^\ 

distillation  of  coal  in- 
side of  gas  retorts), 
which  are  less  fusible, 
are  used  for  terminals. 
For  simple  experi- 
ments, these  pencils  may  be  held  in  forceps  (Fig.  195)  at  the 
ends  of  two  brass  rods,  to  which  the  battery- wires  are  attached. 
These  rods  slide  in  brass  heads  A  and  B,  supported  by  insu- 
lating pillars,  so  that  the  distance  between  the  carbon  points 
may  be  regulated. 

§  234.  Voltaic  arc.  —  The  light  is  too  intense  to  admit  of 
examination  with  the  naked  e}Te  ;  but  if  an  image  of  the  termi- 
nals is  thrown  on  a  screen  by  means  of  a  lens,  or  a  pin-hole  in 


260  ELECTRICITY   AND    MAGNETISM. 

a  card  (see  page  330),  an  arch-shaped  light  is  seen  extending 
from  pole  to  pole,  as  shown  in  Figure  196.  This  light  has 
received  the  name  of  the  voltaic  arc.  The  larger  portion  of  the 
light,  however,  emanates  from  the  tips  of  the  two 
carbon  terminals,  which  are  heated  to  an  intense 
whiteness,  but  some  from  the  arc.  The  -fpole  is 
hotter  than  the  —pole,  as  is  shown  by  its  glowing 
longer  after  the  current  is  stopped.  The  carbon  of 
the  4-pole  becomes  volatilized,  and  the  light-giving 
particles  are  transported  from  the  -f-pc-le  to  the 
—  pole,  forming  a  bridge  of  luminous  vapor  between 
the  poles.  What  we  see  is  not  electricity,  but  luminous  matter. 
Neither  light  nor  a  current  can  exist  without  matter,  as  may  be 
shown  by  trying  to  pass  a  current  between  two  metallic  poles,  a 
little  way  apart,  in  a  charcoal  vacuum  (page  56)  ;  no  spark  can 
be  produced. 

§  235.  Electric  lamp.  —  It  is  apparent  that  the  +pole  is 
subject  to  a  wasting  away,  and  the  —pole  to  a  slight  accession 
of  matter.  At  the  point  of  the  former  a  conical-shaped  cavity 
is  formed,  while  around  the  point  of  the  latter  warty  protuber- 
ances appear.  When,  in  consequence  of  the  wearing  away  of 
the  +pole,  the  distance  between  the  two  pencils  becomes  too 
great  for  the  electric  current  to  span,  the  light  goes  out.  Nu- 
merous self-acting  regulators  for  maintaining  a  uniform  distance 
between  the  poles  have  been  devised.  Such  an  arrangement  is 
called  an  electric  lamp.  In  some,  the  carbons  are  moved  by 
clock-work,  which  requires  winding  up  occasionally ;  in  others, 
the  movement  of  the  carbons  is  accomplished  automatically  by 
the  action  of  the  current  itself. 

§  236.  Electric  candle.  — The  "  Jablochkoff  Candle"  ob. 
viates  all  necessity  for  regulators.  In  this  candle,  instead  of 
the  carbons  pointing  toward  each  other,  they  are  placed  side  by 
side,  a  and  b  (Fig.  197),  separated  by  a  thin  insulating  septum, 


ELECTROTYPING.  261 

c,  of  kaolin.  The  current  passes  up  one  carbon,  across  the 
space  between  the  points,  and  down  the  other.  In  its  passage 
between  the  points  it  forms  the  luminous  arc.  The 
heat  of  the  arc  fuses  and  volatilizes  the  kaolin,  and 
it  wastes  slowly  away  like  the  wick  of  a  candle ; 
hence  its  name. 

The  electric  light  is  of  the  purest  white.  In  it  the 
most  delicate  colors  retain  their  noonday  purity  of 
tint,  while  a  gas  light  appears  of  a  sickly  yellow  hue 
in  comparison. 

§  237.  Electrotyping-. — This  book  is  printed 
from  electrotype  plates.  A  moulding-case  of  brass,  in  the  shape 
of  a  shallow  pan,  is  filled  to  the  depth  of  about  one  centimeter 
with  melted  wax.  A  few  pages  are  set  up  in  common  type,  and 
an  impression  or  mould  is  made  by  pressing  these  into  the  wax. 
The  type  are  then  distributed,  and  again  used  to  set  up  other 
pages.  Powdered  plumbago  is  applied  by  brushes  to  the  sur- 
face of  the  wax  mould  to  render  it  a  conductor.  The  mould  is 
then  flowed  with  alcohol  to  prevent  adhesion  of  air-bubbles,  and 
afterwards  with  a  solution  of  copper  sulphate,  and  dusted  with 
iron  filings,  which  form  by  chemical  action  a  thin  film  of  copper 
on  the  plumbago  surface.  The  case  is  then  suspended  in  a  bath 
of  copper  sulphate  dissolved  in  dilute  sulphuric  acid.  The 
—pole  (why  the  —pole?)  of  a  galvanic  battery  or  magneto  ma- 
chine is  applied  to  it ;  and  from  the  -f  pole  is  suspended  in  the 
bath  a  copper  plate  (why?)  opposite  and  near  to  the  wax  face. 
The  salt  of  copper  is  decomposed  by  the  electric  current,  and 
the  copper  is  deposited  on  the  surface  of  the  mould.  The  sul- 
phuric acid  appears  at  the  -f-pole,  and,  combining  with  the 
copper  of  this  pole,  forms  new  molecules  of  copper  sulphate. 
When  the  copper  film  has  acquired  about  the  thickness  of  an 
ordinary  visiting  card,  it  is  removed  from  the  mould.  This  shell 
shows  distinctly  every  line  of  the  types  or  engraving.  It  is 
then  backed  with  melted  type-metal  to  give  firmness  to  the 


264  ELECTRICITY  AND   MAGNETISM. 

Let  B,  Figure  1,  Plate  III.,  represent  the  message-sender,  or  oper- 
ator's key ;  Y,  the  message-receiver.  It  may  be  seen  that  the  circuit 
is  broken  at  B.  Let  the  operator  press  his  finger  on  the  knob  of  the 
key.  He  closes  the  circuit,  and  the  electric  current  instantly  fills  the 
wire  from  Boston  to  New  York.  It  magnetizes  a ;  a  draws  down  the 
lever  6,  and  presses  the  point  of  a  style  on  a  strip  of  paper  c  that  is 
drawn  over  a  roller.  The  operator  ceases  to  press  upon  the  key,  the 
circuit  is  broken,  and  instantly  b  is  raised  from  the  paper  by  a  spiral 
spring  d.  Let  the  operator  press  upon  the  key  only  for  an  instant,  or 
long  enough  to  count  one,  a  simple  dot  or  indentation  will  be  made  in 
the  paper.  But  if  he  presses  upon  the  key  long  enough  to  count  three, 
the  point  of  the  style  will  remain  in  contact  with  the  paper  the  same 
length  of  time ;  and,  as  the  paper  is  drawn  along  beneath  the  point,  a 
short  straight  line  is  produced.  This  short  line  is  called  a  dash.  These 
dots  and  dashes  constitute  the  alphabet  of  telegraphy.  For  instance,  a 
part  of  a  message,  "  man  is  in,"  is  represented  as  printed  in  tele- 
graphic characters  on  the  strip  of  paper.  The  Roman  letters  above 
interpret  their  meaning. 

§  241.  Sounder.  — If  the  strip  of  paper  is  removed,  and 
the  style  is  allowed  to  strike  the  metallic  roller,  a  sharp  click  is 
heard.  Again,  when  the  lever  is  drawn  up  by  the  spiral  spring, 
it  strikes  a  screw  point  above  (not  represented  in  the  figure) , 
and  another  click,  differing  slightly  in  sound  from  the  first,  is 
heard.  A  listener  is  able  to  distinguish  dots  from  dashes  by 
the  length  of  the  intervals  of  time  that  elapse  between  these 
two  sounds.  Operators  generally  read  by  ear,  giving  heed  to 
the  clicking  sounds  produced  by  the  strokes  of  a  little  hammer. 
A  receiver  so  used  is  called  a  sounder,  a  common  form  of  which 
is  represented  in  the  lower  central  part  of  Plate  III. 

§  242.  Relay  and  repeater.  —  The  strength  of  the  current 
is  diminished,  of  course,  as  the  line  is  extended  and  the  number 
of  instruments  in  the  circuit  is  increased.  Hence,  a  current 
that  would  move  a  single  sounder  audibly,  on  a  short  line, 
would  not  move  many  sounders  on  a  long  line  with  sufficient 
force  to  render  the  message  audible.  Resort  is  had  to  relays 
and  repeaters.  The  principle  on  which  they  remove  this  diffi- 


Plate  III. 


RELAY  AND  REPEATED.  265 

culty  may,  perhaps,  be  best  explained  by  analogy.  In  days  gone 
by,  posts  for  couriers  were  stationed  a  day's  journey  apart. 
At  each  post  were  a  courier  and  a  horse  at  all  hours  ready  to 
start.  The  courier,  bearing  a  dispatch,  rode  all  day,  and  at 
night  reached  a  post  where  fresh  horses  were  saddled  ready  for 
the  next  stage  of  the  journey ;  he  himself  was  exhausted,  his 
force  was  nearly  spent,  but  he  could  awaken  a  courier  who 
was  stationed  there  and  deliver  the  despatches  to  him,  and  he 
with  fresh  strength  instantly  took  up  the  journey.  In  a  similar 
manner  we  picture  to  ourselves  the  electric  current  arriving  at 
a  station  so  nearly  exhausted  that  it  cannot  deliver  intelligible 
signals,  yet  it  may  still  have  strength  to  wake  up  another  bat- 
tery and  set  in  motion  a  fresh  current  which  shall  receive  and 
announce  audibly,  or  carry  forward  the  message  which  the 
exhausted  current  has  just  strength  to  whisper. 

In  Figure  2,  Plate  III.,  the  letter  R  represents  a  relay  and  S  a  sounder. 
Suppose  a  weak  current  arrives  at  New  York  from  Boston,  and  has 
sufficient  strength  to  attract  the  armature  of  the  relay  at  that  station. 
This,  as  may  be  seen  by  examination  of  the  diagram,  will  close  another 
short  circuit,  called  the  local  circuit,  and  send  a  current  from  a  local 
battery  located  in  the  same  office,  through  the  sounder  at  thtit  station. 
The  sounder,  being  operated  by  a  battery  in  a  circuit  of  only  a  few  feet 
in  length,  delivers  the  message  audibly.  If  it  is  desired  that  the  mes- 
sage should  go  beyond  New  York,  —  for  instance,  to  Philadelphia,  — 
then  we  have  only  to  suppose  the  local  line  at  New  York  to  be  length- 
ened so  as  to  extend  to  Philadelphia,  and  a  powerful  line  battery  to  be 
substituted  for  the  small  local ;  then  the  message  that  leaves  Boston  will 
be  shifted  from  one  circuit  to  the  other  at  New  York,  and  be  delivered 
in  Philadelphia  without  the  intervention  of  any  operator  on  the  route. 
In  this  case  a  relay  is  called  a  repeater.  The  electro-magnets  in  relays 
are  wound  with  long  and  thin  wire,  while  those  of  sounders  are  wound 
with  short,  large  wire.  (Explain.  The  main  battery  consists  of  many 
cells ;  how  should  they  be  connected?  It  may  be  located  at  either  ter- 
minus, but  it  is  generally  split  in  halves,  and  one  half  placed  at  each 
terminus ;  how  should  the  two  halves  be  connected  ?) 

In  the  diagram  the  circuit  is  represented  as  open  at  both  keys. 
When  the  line  is  not  in  use,  the  circuit  ought  always  to  be  left  closed, 
by  means  of  switches  connected  with  the  keys  (not  represented  in  the 


266  ELECTRICITY   AND   MAGNETISM. 

diagram),  so  that,  when  the  line  is  not  "at  work,"  an  electric  current 
is  constantly  traversing  the  wire.  Sending  a  message,  consequently, 
consists  in  interrupting  this  current  by  means  of  a  key.  Suppose  that 
Boston  wishes  to  communicate  with  New  York.  He  first  removes  the 
switch  on  his  key,  which  breaks  the  circuit  and  enables  him  to  control 
the  circuit  with  his  key.  He  then  manipulates  his  key  so  as  to  produce 
an  understood  signal,  which  will  attract  New  York's  attention.  Every 
time  that  Boston  presses  on  his  key,  every  armature  in  his  own  office, 
and  in  the  New  York  office,  and  at  way-stations,  falls.  Of  course  the 
message  may  be.  read  at  every  station  on  the  route. 

TELEGRAPHIC  ALPHABET. 


A 

B 

C 

D 

E 

F 

G 

H 

I 

3 

K 

L 

M 

N 

0 

P 

Q 

R 

S 

T 

u 

V 

w 

X 

Y 

Z 

& 

» 

9 

TELEGRAPHIC  FIGURES. 
2345 

7890 


§  243.  Fac-simile  telegraph.  —  This  is  an  autographic  ap- 
paratus by  means  of  which  a  message  may  be,  practicall}-,  trans- 
mitted over  a  wire  and  appear  at  a  distant  terminus  in  the  exact 
hand- writing  of  the  sender,  and  ready  at  once  for  delivery.  The 
principle  on  which  it  operates  may  be  learned  from  the  diagram 
in  Plate  I. ,  in  which  all  details  of  its  mechanism  are  omitted  for 
simplicity  of  illustration.  X  is  a  sheet  of  tin-foil,  on  which  the 
message  to  be  sent  is  written  with  an  ink  prepared  by  dissolving 
sealing-wax  in  alcohol.  The  alcohol  quickly  evaporates,  leaving 
the  lines  of  sealing-wax  adhering  to  the  foil.  Y  is  a  sheet  of 
paper  moistened -with  a  solution  of  prussiate  of  potash.  Each 
of  the  pens  is  simply  a  small,  pointed  iron  needle.  Now  suppose 
that  both  of  the  pens  are  moved  at  the  same  time  and  with  the 


THE   ELECTRIC   FIRE-ALARM. 


267 


same  rapidity  across  their  respective  sheets.  Then  the  electric 
current,  decomposing  the  prussiate  of  potash,  will  cause  the 
needle  in  New  York  to  trace  a  continuous  blue  line  on  Y,  until 
the  needle  in  Boston  reaches  a  line  of  sealing-wax  on  X,  when 
the  circuit  is  broken  as  it  passes  over  this  line.  At  the  same 
time  there  is  a  break  in  the  continuity  of  the  line  traced  on  Y. 
If,  further,  each  needle  is  moved  down  a  hair's  breadth  each 
time  it  traverses  its  respective  sheet,  then  we  shall  have  an 
exact  fac-simile  of  the  writing  on  the  tin-foil  produced  on  the 
chemically-prepared  paper,  except  that  whereas  the  original  is 
written  in  dark  letters  on  a  light  ground,  the  message  is  received 
in  light  letters  on  a  dark  ground.  Pen-and-ink  sketches  of  pho- 
tographs and  other  pictures  may  be  transmitted  in  the  same 
way.  The  pens  are  not,  of  course,  held  and  guided  by  human 
hands,  but  by  complex  machinery.  The  rigorous  exactness 
requisite  in  the  movements  of  the  two  pens  is  secured  by  the 
absolute  synchronism  in  the  vibrations  of  two  pendulums,  one 
at  each  terminus,  controlled  by  the  electric  current. 

Fig.  19D. 


§  244.  The  electric  fire-alarm.  —  This  is  a  modification 
of  the  electro-magnetic  telegraph.  Figure  199  will  serve  to 
illustrate  the  general  plan  of  the  American  system,  invented  by 


268  ELECTRICITY  AND   MAGNETISM. 

Prof.  M.  G.  Farmer,  and  by  him  first  introduced  into  Boston  in 
the  year  1852. 

From  some  central  station  wires  radiate  to  every  part  of  the 
city.  At  suitable  intervals  there  are  inserted  in  these  circuits 
small  cottage-shaped  boxes,  usually  attached  to  buildings  at  the 
corners  of  streets.  On  opening  one  of  these  boxes,  a  person 
who  is  to  give  an  alarm  finds  a  crank  A,  which  he  is  directed  to 
"  pull  down  once  and  let  go."  This  winds  the  spring  H,  which 
sets  in  motion  a  train  of  wheels,  and  causes  a  make-and-break 
wheel  C  to  revolve.  This  wheel  bears  upon  its  circumference 
notches  corresponding  to  the  number  of  the  box.  Two  terminals 
of  the  line  are  so  connected,  one  with  C  and  the  other  with  a 
lever  6,  that  when  the  lever  touches  the  wheel  the  circuit  is 
closed.  But  when  the  wheel  revolves,  and  a  notch  passes  under 
the  lever,  the  circuit  is  broken.  The  effect  of  breaking  the 
circuit  is  to  demagnetize  the  electro-magnet  F  at  the  central 
station,  and  release  the  armature  which  is  attached  to  the 
tongue  of  a  bell.  The  tongue  then  being  drawn  forcibly  by 
the  spring  G  in  the  opposite  direction,  produces  one  stroke  on 
the  bell.  By  pulling  the  lever  down  once,  the  spring  is  wound 
up  just  enough  to  cause  C  to  revolve  three  times,  and  thus  the 
number  of  the  box  is  struck  three  times  in  succession.  The 
watchman  at  the  central  station,  being  thus  notified  of  the 
existence  and  locality  of  the  fire,  at  once  and  in  a  similar  man- 
ner notifies  the  several  fire-engine  companies. 

XXXVII.     TELEPHONE   AND   MICROPHONE. 

§  245.  Bell  telephone.  —  Figure  200  represents  a  sectional  and 
a  perspective  view  of  this  instrument.  It  consists  of  a  steel  magnet 
A,  encircled  at  one  extremity  by  a  spool  B  of  very  fine  iusulated  wire, 
the  ends  of  which  are  connected  with  the  binding  screws  DD.  Im- 
mediately in  front  of  the  magnet  is  a  thin  circular  iron  disk  EE.  The 
whole  is  enclosed  in  a  wooden  or  rubber  case  F.  The  conical-shaped 
cavity  G  serves  the  purpose  of  either  a  mouth-piece  or  an  ear-trumpet. 
There  is  no  difference  between  the  transmitting  and  receiving  tele- 
phone;  consequently  either  instrument  may  be  employed  as  a  trans- 
mitter, while  the  other  serves  as  a  receiver.  Two  magneto  telephones 


BELL  TELEPHONE.  269 

in  a  circuit,  are  virtually  in  the  relation  of  a  magneto-electric  generator 
and  a  motor.  The  transmitter  being  in  itself  a  diminutive  magneto 
machine,  of  course  no  battery  is  required  in  the  circuit.  Connect  in 
circuit  two  such  telephones,  and  the  apparatus  is  ready  for  use. 


When  a  person  talks  to  the  disk  of  the  transmitter,  he  throws  it 
into  rapid  vibration.  The  disk,  being  quite  close  to  the  magnet,  is 
magnetized  by  induction;  and,  as  it  vibrates,  its  magnetic  power 
is  constantly  changing,  being  strengthened  as  it  approaches  the 
magnet,  and  enfeebled  as  it  recedes.  This  fluctuating  magnetic  force 
will  of  course  induce  currents  in  alternate  directions  in  the  neighboring 
coil  of  wire.  These  currents  traverse  the  whole  length  of  the  wire, 
and  so  pass  through  the  coil  of  the  distant  instrument.  When  the 
direction  of  the  arriving  current  is  such  as  to  reenforce  the  power  of 
the  magnet  of  the  receiver,  the  magnet  attracts  the  iron  disk  in  front 
of  it  more  strongly  than  before.  If  the  current  is  in  the  opposite 
direction,  the  disk  is  less  attracted,  and  flies  back.  Hence,  whatever 
movement  is  imparted  to  the  disk  of  the  transmitting  telephone,  the 
disk  of  the  receiving  telephone  is  forced  to  repeat.  The  vibrations  of 
the  latter  disk  become  sound  in  the  same  manner  as  the  vibrations  of 
a  tuning  fork  or  the  head  of  a  drum. 

The  above  is  a  description  of  the  original  and  simplest  form  of  the 
Bell  telephone.  It  is  apparent  that  the  original  energy,  i.e.,  that  of 
the  voice,  applied  at  the  transmitter  must,  during  its  successive  trans- 
formations and  especially  during  its  transmission  in  the  form  of 
electric  energy  through  large  resistances,  become  very  much  en- 


270 


ELECTRICITY   AND   MAGNECTISM. 


feebled,  so  that  when  it  reappears  as  sound,  the  sound  is  quite  feeble 
and  frequently  inaudible.  The  first  grand  improvement  on  the  original 
consists  in  introducing  a  battery  into  the  circuit  and  so  arranging  that 
the  voice  instead  of  being  obliged  to  generate  currents  should  be 
required  to  act  only  as  a  controlling  force  of  a  current  already 

Fig.  200  a. 


Fig.  200  b. 


generated  by  the  battery.  It  is  evident  that  only  a  fluctuating 
or  undulating  current  can  produce  the  necessary  vibrations  in  the 
disk  of  the  receiver.  The  fluctuations  are  caused  by  a  varying  resist- 
ance in  the  circuit.  The  pupil  must  have  learned  by  experience  ere 
this  that  the  effect  of  a  loose  contact  between  any  two  parts  of  a 
circuit  is  to  increase  the  resistance  and  thereby  weaken  the  current ; 
but  the  effect  of  a  slight  variation  in  pressure  is  especially  noticeable 
when  either  or  both  of  the  parts  are  carbon.  Figure  200  a  illustrates  a 
simple  telephonic  circuit  in  which  are  included  a  variable  resistance 
transmitter  T,  a  magneto  receiver  E,  and  a  battery  B.  One  of  the 
electrodes,  a  platinum  point,  touches  the  center  of  the  transmitter 
disk;  the  other  electrode,  a  carbon  button  a,  is  pressed  by  a  spring 
gently  against  the  platinum  point.  Every  vibration  of  the  disk,  how- 
ever minute,  causes  a  variation  in  the  pressure  between  the  two 
electrodes  and  a  corresponding  variation  in  the  circuit  resistance. 
As  changes  the  resistance,  so  changes  the  current  strength,  and  so 
consequently  changes  the  force  with  which  the  magnet  in  the  receiver 


MICROPHONE.  271 

R  pulls  its  disk.    The  varying  tension  between  magnet  and  disk 
causes  the  latter  to  vibrate  and  reproduce  sounds. 

The  next  improvement  of  considerable  importance  consists  in  the 
adoption  of  an  induction  coil,  which,  we  have  learned,  produces  a 
current  of  much  greater  force  than  is  possessed  by  the  original 
battery  current.  By  its  adoption  we  are  able  to  converse  over 
much  longer  distances,  and  since  the  battery  current  traverses  only 
a  local  circuit,  as  may  be  seen  by  reference  to  Fig.  200  6,  a  single 
Leclanche  cell  is  generally  sufficient  to  operate  it.  The  currents 
induced  by  the  fluctuating  primary  current  traverse  the  line  wire  and 
generate  sonorous  vibrations  in  the  disk  of  the  receiver  in  the  same 
manner  as  in  the  original  telephone. 


Fig.  201. 


§  246.  Microphone.  —  In  Figure  201,  A  and  B  are  buttons  of 
carbon ;  the  former  is  attached  to  a  sounding-board  of  thin  pine  wood, 
the  latter  to  a  steel  spring  C,  and  both  are  connected  in  circuit  with  a 
battery  and  a  telephone  used  as  a  receiver.  The  spring  presses  B 
against  A,  and  any  slight  jar  will  cause  a  variation  in  the  pressure  and 
corresponding  variations  in  the  current  strength. 

By  means  of  this  instrument,  called  the  microphone,  any  little  sounds, 
as  its  name  indicates,  such  as  the  ticking  of  a  watch  or  the  footfall  of 
an  insect,  mny  be  reproduced  at  a  considerable  distance,  and  be  as 
audible  as  though  the  original  sounds  were  made  close  to  the  ear. 


CHAPTER    V. 
SOUND. 

THE  subjects  of  Sound  and  Light,  which  we  have  now  to 
study,  have  two  important  characteristics  in  common  that  dis- 
tinguish them  from  the  subjects  already  studied.  First,  each  of 
them  affects  its  peculiar  organ  of  sense,  the  ear  or  eye,  and 
very  many  of  the  phenomena  to  be  studied  under  each  subject 
are  of  importance  only  to  one  or  the  other  of  these  senses ; 
while  the  most  common,  and  many  of  the  most  important  appli- 
cations of  heat  and  electricity  have  no  direct  relation  to  any 
organ  of  sense.  Second,  both  sound  and  light,  we  shall  find 
originate  in  vibrating  bodies,  and  reach  us  only  by  the  inter- 
vention of  some  medium  capable  of  being  set  in  vibration. 

Here,  as  in  all  other  kinds  of  motion,  energy  is  involved ;  the 
ear  or  eye  absorbs  energy  whenever  a  sensation  is  produced,  but 
the  amount  absorbed  is  so  minute,  and  the  difficulty  of  measuring 
it  so  great,  that  usually  other  points  better  deserve  the  student's 
attention. 

Let  us  begin  with  the  study  of  such  vibrations  as  will  neither 
produce  sound,  nor  in  a  dark  room  affect  the  eye. 

XXXVIII.     VIBRATION   AND  WAVES. 

§  247.  Vibration.  —  Experiment  1.  Kepeat  the  experiment  with 
the  pendulum  lm  long,  page  111,  and  note  in  what  respects  its  motion 
differs  from  most  other  motions. 

Experiment  2.  Take  a  pendulum  50cm  long,  hold  it  with  the  string 
just  touching  an  edge  of  a  table,  having  the  hand  about  38cm  above  the 
table,  and  set  it  vibrating ;  the  ball  will  be  seen  to  vibrate  faster  in  the 
portion  of  its  arc  that  is  under  the  table  than  in  the  other  portion,  and 
so  more  vibrations  are  made  in  ten  seconds  than  if  the  string  swing 
freely  without  touching  the  table. 


DIRECTION  OF   VIBRATION.  273 

Experiment  3.  Without  the  pendulum,  move  the  hand  quickly  from 
side  to  side  every  two  seconds,  turning  instantly  at  one  side,  and  wait- 
ing at  the  other  till  the  two  seconds  are  up. 

These  three  motions,  though  very  different,  have  this  in  com- 
mon :  the  motions  in  each  case  occur  at  equal  intervals  of  time. 
This  interval  of  time  is  called  the  period  of  vibration.  In  Exp.  1 
it  was  two  seconds  ;  in  Exp.  2,  about  one  second ;  and  in  Exp.  3, 
two  seconds.  The  motion  from  one  side  to  the  other  and  back 
is  called  a  vibration.  If  n  =  the  number  of  vibrations  in  one 

second,  and  t  =  the  period,  t= —    The  amplitude  of  pendulum 

n 

vibrations  is  assumed  to  be  very  small.  In  Exp.  1  the  motion  is 
called  a  simple  (or  pendular)  vibration;  in  the  other  cases  the 
vibration  of  the  ball  or  the  hand  is  complex.  Do  not  confound 
period  with  duration  of  the  vibrating  state ;  in  Exp.  1  the 
pendulum  may  have  vibrated  ten  or  one  hundred  seconds, 
before  coming  to  rest,  but  the  period  was  two  seconds.  Con- 
sidered mathematically,  other  periodic  (and  therefore  vibratory) 
motions  are,  the  movements  of  the  hands  of  a  watch,  the  regu- 
lar trips  of  a  stage-coach,  etc.  A  vibration  is  a  recurrent  change 
of  position. 

§  248.  Direction  of  vibration.  —  A  small  rod,  like  a  yard- 
stick, fixed  at  one  end,  may  be  set  in  vibration  by  pulling  the 
other  end  to  one  side  ;  a  tree  vibrates  in  the  wind  ;  the  strings 
of  a  piano  swing  from  side  to  side  when  vibrating  ;  in  all  these 
cases  the  motion  is  at  right  angles  to  the  length  of  the  body, 
and  so  the  body  is  bent.  These  are  all  cases  of  transverse 
vibrations. 

Experiment.  Hang  up  a  spiral  spring,  or  elastic  cord,  with  a  weight 
attached  to  the  lower  end;  lift  the  weight,  and,  dropping  it,  notice 
that  the  cord  vibrates,  lengthening  and  shortening  rapidly. 

The  motion  of  the  body  is  in  the  direction  of  its  length,  and 
so  it  is  not  bent ;  this  is  a  case  of  longitudinal  vibration.  Twist 
the  string,  and  see  that  it  is  possible  to  set  up  torsional  vibra- 


274  SOUND. 

tions.     Compare  these  kinds  of  vibration  with   the   kinds   of 
elasticity  studied  on  page  30. 

§  249.  Propagation  of  vibration.  —  Waves.  —  Expert- 
iiieiit.  Take  a  soft  cotton  rope,  a  few  meters  long,  lay  it  straight  on 
a  floor,  set  one  end  in  vibration  by  quick  movements  of  the  hand. 
Notice  any  point  hi  the  rope,  and  see  that  it  is  set  in  vibration;  that 
is,  it  moves  up  and  down,  or  laterally  from  side  to  side  through  its 
original  position  of  rest.  Make  a  single  movement  of  the  hand,  which 
is  better  called  a  pulse  than  a  vibration ;  it  is  easy  to  see  that  the 
pulse  does  not  reach  all  points  of  the  rope  at  the  same  time.  Send  a 
quick  succession  of  equal  pulses  along  the  rope ;  at  any  instant  differ- 
ent pulses  affect  different  parts  of  it,  and  you  get  more  or  less  perfectly 
the  familiar  form  that  we  call  a  wave-line.  Notice  that  any  point  of 
the  rope  only  moves  up  and  down,  while  the  form  of  the  wave  moves 
on.  Vibrate  the  hand  in  a  longer  period,  and  notice  that  the  distance 
from  crest  to  crest  is  longer  than  before. 

§  250.  Wave-length  and  amplitude.  —  Imagine  an  in- 
stantaneous photograph  taken  of  the  rope  along  which  the  waves 

are  passing.  It  would  appeal- 
much  like  the  curved  line  CD, 
Figure  202.  This  curve  repre- 
sents what  is  known  as  a  simple 
wave-line.  The  shortest  of  the 
similar  portions  into  which  a 
wave-line  can  be  cut  is  called  a  wave-length,  as  wx,  uv,  or  en. 
The  greatest  distance  of  any  point  in  a  wave  from  the  axis,  as 
ow,  is  called  the  amplitude  of  the  wave. 

§  251.  Reflection  of  waves.  —  Interference.1  —  Experi- 
ment 1.  Stretch  the  rope  horizontally  between  two  elevated  points, 
and  pluck  it  with  the  hand  or  strike  it  with  a  stick  near  one  end,  and 
send  along  it  a  single  pulse,  forming  a  crest  on  the  rope  (A,  Fig. 
203).  This  travels  to  the  other  end,  and  there  we  see  it  reflected  and 
inverted  (B). 

1  See  Section  G  of  the  Appendix. 


STATIONARY   VIBRATIONS,    ETC. 


275 


Fig.  203. 


Experiment  2.  Just  at  the  instant  of  reflection,  start  a  second 
crest;  these  two,  the  crest  and  the  returning  inverted  crest  or  trough 
(C),  are  now  traveling 
along  the  rope  in  oppo- 
site directions,  and  must 
meet  at  some  point.  This 
point  will  be  urged  up- 
ward by  the  crest  and 
downward  by  the  trough, 
and  so  its  motion  will  be 
due  to  the  difference  of 
the  two  forces. 

Experiment  3.  Send 
along  the  rope,  first  a  trough,  then  a  crest;  now  two  crests  (D)  will 
meet  near  the  middle  of  the  rope,  and  the  motion  here  will  be  due  to 
two  forces  acting  in  the  same  direction,  and  so  the  resulting  crest  will 
be  greater  than  either  of  the  original  ones. 

This  action  on  a  single  point  of  two  pulses,  or  two  trains  of 
waves,  no  matter  if  from  different  sources,  is  termed  interfer- 
ence. The  resulting  motion  may  be  greater  or  less  than  that 
due  to  either  pulse  alone,  or  it  may  be  zero. 

§  252.   Stationary  vibrations,  nodes,  etc.  —  Experiment. 

Hold  one  end  of  a  rubber  tube,  about  2m  long,  while  the  other  is  fixed, 
and  send  along  it  a  regular  succession  of  equal  pulses  from  the  vibrat- 
ing hand;  it  will  be  easy,  by  varying  the  tension  a  little,  to  obtain  a 
succession  of  gauzy  spindles  (Fig.  204)  separated  by  points  that  are 

Fig.  204. 


nearly  or  quite  at  rest.  Unlike  the  earlier  experiments,  the  waves  here 
do  not  appear  to  travel  along  the  tube ;  yet  in  reality  they  do  traverse 
it.  The  deception  is  caused  by  stationary  points  being  produced  by  the 
interference  of  the  advancing  and  retreating  waves. 

This  interference  of  direct  and  reflected  waves  gives  rise  to 
the   important   class   of  so-called  stationary  vibrations.     The 


276  SOUND. 

points  of  least  motion,  as  a  and  6,  are  called  nodes;  the  points 
of  greatest  motion,  c  and  d,  are  called  antmodes;  and  the  por- 
tion of  the  rope  between  a  node  and  an  antinode,  as  ac,  is  a 
semi-ventral  segment,  and  ab  is  a  ventral  segment. 

§  253.  Water-waves.  —  If  you  have  a  long  and  rather 
narrow  box  or  trough,  nearly  filled  with  water,  you  can  pro- 
duce much  the  same  effects  as  with  the  rope.  A  crest  is 
caused  by  thrusting  the  hand  into  the  water  ;  a  trough,  by  sud- 
denly withdrawing  it.  Chips  floating  on  the  water  show  that 
here,  as  with  the  rope,  it  is  only  a  form  that  advances  —  not 
the  matter.  But  more  careful  observation  will  show  that  the 
chip,  when  on  the  crest  of  the  wave,  does  move  forward  a  little, 
and  when  in  the  trough  moves  backward  a  little ;  thus  it  does 
not  merely  rise  and  fall,  but  goes  round  in  a  curve  that  is 
approximately  a  circle.  After  a  little  practice,  you  may  be  able 
to  produce  interference  and  stationary  waves  ;  or  you  may  pro- 
duce them  by  blowing  on  the  surface  of  water  in  a  basin,  or  by 
tapping  the  basin.  Water-waves  furnish  important  illustrations 
of  the  fact  that  energy  may  be  transmitted  by  vibration  as  truly 
as  by  the  actual  transfer  of  the  medium,  as  in  the  river's  current 
or  the  wind. 

§  254.   Longitudinal  waves.  —  Experiment.   Procure  a  brass 
wire  wound  in  the  form  of  a  spiral  spring,1  about  4m  long.     Attach  one 
end  to  a  cigar  box,  and  fasten  the  box  to  a  table.   Hold  the  other  end  H 
of  the  spiral  firmly  in  one  hand,  and  with  the  other  hand  insert  a  knife- 
blade  between  the 

Fig.  205.^  ^  turns  of  the  wire, 

and  quickly  rake 
it  for  a  short  dis- 
tance along  the 
spiral  toward  the 

box,  thereby  crowding  closer  together  for  a  little  distance  (B,  Fig. 
205)  the  turns  of  wire  in  front  of  the  hand,  and  leaving  the  turns 
behind  pulled  wider  apart  (A)  for  about  an  equal  distance.  The 

1  About  25m  of  No.  20  brass  spring-wire  should  be  wound  with  care  in  a  lathe  on  a 
spindle  lcm  in  diameter,  as  close  as  possible. 


AIR   AS   A  MEDIUM   OF   WAVE-MOTION.  277 

/ 

crowded  part  of  the  spiral  may  be  called  a  condensation,  and  the 
stretched  part  a  rarefaction.  The  condensation,  followed  by  the  rare- 
faction, runs  with  great  velocity  through  the  spiral,  strikes  the  box,  pro- 
ducing a  sharp,  loud  blow;  is  reflected  from  the  box  back  to  the  hand, 
and  from  the  hand  again  to  the  box,  producing  a  second  blow ;  and  by 
skilful  manipulation  three  or  four  blows  may  be  produced  in  rapid  suc- 
cession. If  a  piece  of  twine  be  tied  to  some  turn  of  the  wire,  it  will 
be  seen,  as  each  wave  passes  it,  to  receive  a  slight  jerking  movement 
forward  and  backward  in  the  direction  of  the  length  of  the  spiral. 

How  is  energy  transmitted  through  these  4m  of  spring  so  as 
to  deliver  the  blow  on  the  box?  Certainly  not  by  a  bodily 
movement  of  the  spiral  as  a  whole,  as  might  be  the  case  if  it 
were  a  rigid  rod.  The  movement  of  the  twine  shows  that  the 
only  motion  which  the  coil  undergoes  is  a  vibratory  movement 
of  its  turns.  Here,  as  in  the  case  of  water-waves,  energy  is 
transmitted  through  a  medium  by  the  transmission  of  vibrations. 

There  are  two  important  distinctions  between  this  kind  of 
wave  and  a  liquid  wave  :  the  former  consists  of  a  condensation 
and  a  rarefaction  ;  the  latter,  of  an  elevation  and  a  depression  ; 
in  the  former,  the  vibration  of  the  parts  is  in  the  same  line  with 
the  path  of  the  wave,  and  hence  these  are  called  longitudinal 
waves;  in  the  latter,  across  its  path,  and  they  are  therefore 
transverse  waves. 

A  wave  cannot  be  transmitted  through  an  inelastic  soft  iron 
spiral.  Elasticity  is  essential  in  a  medium,  that  it  may  transmit, 
waves  made  up  of  condensations  and  rarefactions;  and  the  greater 
the  elasticity,  the  greater  the  facility  and  rapidity  with  which  a 
medium  transmits  waves. 

§  255.  Air  as  a  medium  of  wave-motion.  —  May  not  air 
and  other  gases,  which  are  elastic,  serve  as  media  for  waves? 

Experiment.  Place  a  candle  flame  at  the  orifice  a  of  the  tube,1  Figure 
206,  and  strike  the  table  a  sharp  blow  with  a  book  near  the  orifice  6. 

1  This  tube,  which  will  serve  many  important  purposes,  may  be  made  of  tin  in  three 
parts,  A  and  B,  each  2.5m  long,  and  10°™  in  diameter,  and  a  conical-shaped  cap  C  about 
30cm  long,  having  an  orifice  of  3cm  diameter.  The  ends  of  the  three  parts  should  be 
made  slightly  tapering,  so  that  they  may  bo  put  together  like  a  stove-pipe. 


278  SOUND. 

Instantly  the  candle  flame  is  quenched.  The  body  of  air  in  the  tube 
serves  as  a  medium  for  transmission  of  motion  to  the  candle. 

Was  it  the  motion  of  a  current  of  air  through  the  tube,  as  when 
blown  through,  or  was  it  the  transfer  of  a  vibratory  motion?  Burn 
touch-paper  *  at  the  orifice  ft,  so  as  to  fill  this  end  of  the  tube  with 
smoke,  and  repeat  the  last  experiment. 

Evidently,  if  the  body  of  air  is  moved  along  through  the  tube,  the 
smoke  will  be  carried  along  with  it.  The  candle  is  blown  out  as  before, 
but  no  smoke  issues  from  the  orifice  a.  It  is  clear  that  there  is  no 


Fig.  206. 


translation  of  material  particles  from  one  end  to  the  other,  —  nothing 
like  the  flight  of  a  rifle  bullet.  The  candle  flame  was  struck  by  some- 
thing like  a  pulse  of  air,  and  not  by  a  wind. 

§  256.  How  a  wave  is  propagated  through  a  medium. 
—  The  effect  of  applying  force  with  the  hand  to  the  spiral 
spring  is  to  produce  in  a  certain  section  (B,  Fig.  205)  of  the 
spiral  a  crowding  together  of  the  turns  of  wire,  and  at  A  a 
separation  ;  but  the  elasticity  of  the  spiral  instantly  causes  B  to 
expand,  the  effect  of  which  is  to  produce  a  crowding  together  of 
the  turns  of  wire  in  front  of  it,  in  the  section  C,  and  thus  a  for- 
ward movement  of  the  condensation  is  made.  At  the  same 
time,  the  expansion  of  B  causes  a  filling  up  of  the  rarefaction  a 
A,  so  that  this  section  is  restored  to  its  normal  state.  This  it 
not  all :  the  folds  in  the  section  B  do  not  stop  in  their  swing 
when  they  have  recovered  their  original  position,  but,  like  a 
pendulum,  swing  beyond  the  position  of  rest,  thus  producing  a 
rarefaction  at  B,  where,  immediately  before,  there  was  a  con- 

1  To  prepare  touch-paper,  dissolve  about  a  teaspoonful  of  saltpeter  in  a  half  teacupfu] 
of  hot  water,  dip  unsized  paper  in  the  solution,  and  then  allow  it  to  dry.  The  paper  pro- 
duces much  smoke  in  burning,  but  no  flame. 


HOW  A  WAVE-LINE  REPKESENTS  A  VIBKATION.        279 

densation.  Thus  a  forward  movement  of  the  rarefaction  is 
made,  and  thus  a  pulse  or  wave  is  transmitted  with  uniform 
velocity  through  a  spiral  spring,  air,  or  any  elastic  medium. 

§  257.   How  a  wave-line  represents  a  vibration.  —  We 

saw  (page  274)  that  a  wave  might  be  caused  by  a  vibration, 
and  readily  believe  that  if  the  vibration  is  changed  in  any  way, 
the  wave  must  show  some  corresponding  change.  In  fact  the 
wave-line  shows  at  once  something  about  the  vibration  for  sev- 
eral successive  periods ;  so,  if  we  could  attach  a  cord  to  a 
vibrating  body,  or  set  up  vibrations  in  water  by  it,  and  then 
take  an  instantaneous  photograph  of  the  rapidly-disappearing 
waves,  we  might  learn  much  about  the  nature  of  the  original 
vibrations. 

A  much  more  practical  arrangement,  which  gives  a  permanent 
wave-line,  is  the  following 

Experiment.  Attach,  by  means  of  sealing-wax,  a  bristle  or  a  fine 
wire  to  the  end  of  one  of  the  prongs  of  a  tuning-fork,  as  seen  in 
Figure  207.  Set  the  fork  in  Fig  2Q7 

vibration,  and  quickly  draw 
the  point  of  the  bristle 
lightly  over  a  smoked  glass 
(A,  Fig.  207).  A  beautiful  wavy  line  will  be  traced  on  the  glass,  each 
wave  corresponding  to  a  vibration  of  the  prong  when  vibrating  as  a 
whole. 

Next  tap  the  fork,  near  its  stem,  on  the  edge  of  a  table,  and  trace  its 
vibrations  on  a  smoked  glass  as  before.  You  will  generate  the  same 
set  of  waves  that  you  did  before ;  but,  running  over  these,  is  another  set 
of  waves,  of  much  shorter  period,  much  like  No.  3  of  Figure  223,  page 
312,  showing  that  the  prong  vibrates,  not  only  as  a  whole,  but  in  parts. 
The  serrated  wavy  line  produced  represents  the  resultant  of  the  com- 
bined vibrations,  and  may  be  called  a  complex  wave-line. 

If  we  imagine  the  piece  of  twine  on  the  spiral  (page  277) 
replaced  by  a  bristle  pointing  downward,  and  under  it  a  smoked 
glass  drawn  at  right  angles  to  the  length  of  the  spiral,  the 
vibrating  bristle  will  trace  a  characteristic  curve  on  the  glass. 
We  may  even  conceive  a  writing  point  attached  to  a  particle 


280  SOUND. 

of  air  and  tracing  these  curves,  and  thus  understand  how  it 
can  illustrate  the  nature  of  the  vibration  of  the  air.  This  method 
is  known  as  the  graphical  method  of  studying  vibrations. 

XXXIX.     SOUND-WAVES. 

§  258.  How  sound  originates.  —  Listen  to  yonder  sound- 
ing church-bell.  It  produces  a  sensation  ;  it  is  heard.  If  the 
orifices  of  the  ears  be  stopped  by  pressing  the  palms  of  the 
hands  against  them,  the  sensation,  in  a  great  measure,  ceases. 
The  ear  is,  therefore,  the  organ  of  sense  through  which  the 
sensation  of  hearing  is  produced.  The  bell  must  be  the  cause 
of  the  impression  made  on  the  ear.  But  the  bell  is  at  such  a 
distance  that  it  cannot  itself  act  on  the  ear  ;  yet  something  must 
act  on  the  ear,  and  it  must  be  the  bell  which  causes  that  some- 
thing to  act. 

Commencing  at  the  origin  of  sound,  let  the  first  inquiry  be, 
How  does  a  sounding  bod}1-  differ  from  a  silent  body  ? 

Experiments.  Strike  a  bell  or  a  glass  bell-jar,  and  touch  the  edge 
with  a  small  cork  ball  suspended  by  a  thread ;  you  not  only  hear  the 
sound,  but,  at  the  same  time,  you  see  a  tremulous  motion  of  the  ball, 
caused  by  a  motion  of  the  bell.  Touch  the  bell  gently  with  a  finger, 
and  you  feel  a  tremulous  motion.  Press  the  hand  against  the  bell ; 
you  stop  its  vibratory  motion,  and  at  that  instant  the  sound  ceases. 
Strike  the  prongs  of  a  tuning-fork,  press  the  stem  against  a  table,  you 
hear  a  sound.  Touch  gently  the  cheek  with  the  end  of  one  of  the 
prongs  ;  you  feel  a  tickling  sensation  produced  by  its  minute  vibrations. 
Thrust  the  ends  of  the  prongs  just  beneath  the  surface  of  water ;  the 
water  is  thrown  off  in  a  fine  spray  on  either  side  of  the  vibrating  fork. 
Watch  the  strings  of  a  piano,  guitar,  or  violin,  or  the  tongue  of  a  jews- 
harp,  when  sounding.  You  can  see  that  they  are  in  motion. 

The  difference  between  a  body  when  sounding  and  when  not 
sounding  is,  that  when  sounding  it  is  in  a  state  of  continuous 
vibration  ;  when  not  sounding,  this  vibration  is  absent,  and  the 
parts  of  the  body  are  at  rest  among  themselves.  We  conclude 
that  sound  originates  in  a  vibrating  body. 


HOW   SOUND   TRAVELS.  281 

Sounds  that  proceed  from  the  tuning-fork  and  the  violin 
string  are  examples  of  sound  produced  by  transverse  vibrations. 

Experiment  1.  With  one  hand  grasp  at  its  center  a  glass  tube 
about  lm  long ;  lay  a  damp  woolen  cloth  on  the  palm  of  the  other  hand, 
and  grasp  the  tube  tightly  with  this  hand,  and  slide  it  quickly  length- 
wise the  tube.  The  friction  between  the  cloth  and  the  tube  will  throw 
the  latter  into  longitudinal  vibrations,  and  a  loud,  shrill  sound  will  be 
produced. 

Experiment  2.  Take  a  strip  of  sheet-iron  or  brass  15cm  long  and 
gem  \vide,  make  a  hole  near  one  end,  and  suspend  by  a  string  lm  long 
from  the  hand,  and  rotate  it  rapidly  about  the  hand  after  the  manner 
of  a  sling.  The  string  will  rapidly  twist  and  untwist,  and  a  loud  sound 
will  result  from  the  torsional  vibrations. 

§  259.  How  sound  travels.  —  How  can  a  bell,  sounding 
at  a  distance,  affect  the  ear?  If  the  bell  while  sounding  pos- 
sesses no  peculiar  property  except  motion,  then  it  has  nothing 
to  communicate  to  the  ear  but  motion.  But  motion  can  be 
communicated  by  one  body  to  another  at  a  distance  only  through 
some  medium. 

Does  sound  require  a  medium  for  its  communication  ?  If  so, 
what  is  the  medium  ? 

Experiment.  Lay  a  thick  tuft  of  cotton-wool  on  the  plate  of  an 
air-pump,  and  on  this,  face  downward,  place  a  loud-ticking  watch,  and 
cover  with  the  receiver.  Notice  that  the  receiver,  interposed  between 
the  watch  and  your  ear,  greatly  diminishes  the  sound,  or  interferes 
with  the  passage  of  something  to  the  ear.  Take  a  few  strokes  of  the 
pump  and  listen ;  the  sound  is  more  feeble,  and  continues  to  grow  less 
and  less  distinct  as  the  exhaustion  progresses,  until  either  no  sound 
can  be  heard  when  the  ear  is  placed  close  to  the  receiver,  or  an  ex- 
tremely faint  one,  as  if  coming  from  a  great  distance.  The  removal 
of  air  from  a  portion  of  the  space  between  the  watch  and  your  ear 
destroys  the  sound,  although  the  watch  continues  to  tick.  Let  in  the 
air  again  and  the  sound  is  restored. 

Thus  it  appears  that  sound  cannot  travel  through  a  vacuum  ;  in 

other  words,  without  a  medium,  and  the  medium  in  this  case  is  air. 

By  which  of  the  two  methods  described  on  page  278  is  mo- 


282  SOUND. 

tion  transmitted  from  the  sounding  bod}'  through  the  air?  Take 
an  extreme  case  :  A  cannon  is  discharged  at  a  distance  of  one- 
fourth  of  a  mile  from  you.  You  not  only  hear  the  sound,  but 
feel  the  shock  communicated  by  the  air ;  the  windows  are 
shaken  by  it ;  at  the  same  time,  you  easily  perceive  that  it  is 
not  the  motion  of  a  wind,  but  the  motion  of  a  pulse.  It  can 
easily  be  shown  that  the  pulse  travelled  at  a  rate  of  about  800 
miles  in  an  hour,  or  with  nearly  the  velocity  of  a  rifle  ball, 
whereas  the  wind  of  a  hurricane  seldom  exceeds  75  miles  an 
hour.  What,  think  you,  would  be  the  result  if  you  were  to  be 
struck  b}r  a  gust  of  wind  of  such  velocity?  Yet  the  softest 
whisper  travels  with  ver}T  nearly  the  same  speed. 

§  260.  Air-waves. — Boys  amuse  themselves  by  inflating 
paper  bags,  and  with  a  quick  blow  bursting  them,  producing 
with  each  a  single  loud  report.  First  the  air  is  suddenly  and 
greatly  condensed  by  the  blow,  the  bag  is  burst ;  the  air  now,  as 
suddenly  and  with  equal  force,  expands,  and  by  its  expansion 
condenses  the  air  for  a  certain  distance  all  around  it,  leaving  a 
rarefaction  where  just  before  had  been  a  condensation.  If  many 
bags  were  burst  at  the  same  spot  in  rapid  succession,  the  result 
would  be  that  alternating  shells  of  condensation  and  rarefaction 
would  be  thrown  off,  all  having  a  common  center,  enlarging  as 
the}7  advance,  like  the  waves  formed  by  stones  dropped  into 
water ;  only  that,  in  this  case,  the  waves  are  not  like  rings,  but 
hollow  globes  ;  not  circular,  but  spherical. 

As  a  wave  advances,  each  individual  air-particle  concerned  in 
its  transmission  performs  a  short  excursion  fro  and  to  in  a 
straight  line  radiating  from  the  center  of  the  shells  or  hollow 
globes.  A  particle  begins  to  move  when  the  front  of  the  shell 
of  compression  touches  it,  and  completes  its  motion  when  the 
back  of  the  next  shell  of  rarefaction  leaves  it.  Accordingly,  an 
air-wave  travels  its  own  length  in  the  time  that  a  particle  occupies 
in  going  through  one  complete  vibration  so  as  to  be  ready  to  start 
again. 


SOLIDS   AND   LIQUIDS   AS   MEDIA   OF   SOUND.         283 

§  261.  What  sound  is.  —  The  term  sound  is  sometimes 
used  to  denote  a  sensation,  sometimes  to  denote  the  external 
cause  of  the  sensation  ;  it  is  in  this  latter  sense  that  the  word  is 
used  in  Physics,  and  that  we  have  to  define  it. 

If  the  ear  replace  the  candle  in  the  experiment  (page  278) ,  the 
air  pulse  produces  a  loud  sound.  Conversely,  air-waves  started 
by  the  voice  may  affect  a  flame,  as  shown  on  page  313.  In  fact, 
the  relation  between  the  cause  of  our  sensation  and  a  vibration 
is  so  uniform,  that  we  may  say,  Sound  is  vibration  that  may  be 
appreciated  by  the  ear: 

§  262.  Solids  and  liquids  as  media  transmitting  sound. 
—  Experiment  1.  Lay  a  watch,  with  its  back  downward,  on  and  near 
to  one  end  of  a  long  board  (or  table),  and  cover  the  watch  with  loose 
folds  of  cloth  till  its  ticking  cannot  be  heard  through  the  air  in  any 
direction  at  a  distance  equal  to  the  length  of  the  board.  Now  place 
the  ear  in  contact  with  the  distant  end  of  the  board,  and  you  will  hear 
the  ticking  of  the  watch  very  distinctly. 

Experiment  2.  Place  one  end  of  a  long  pole  on  a  resonance  box 
(page  296),  ar.d  apply  the  stem  of  a  vibrating  tuning-fork  to  the  other 
end ;  the  sound-vibrations  will  be  transmitted  through  the  pole  to  the 
box,  and  a  loud  sound  will  be  given  out  by  the  box,  as  though  that, 
and  not  the  tuning-fork,  were  the  origin  of  the  sound. 

Experiment  3.  Place  the  ear  to  the  earth,  and  listen  to  the  rumbling 
of  a  distant  carriage ;  or  put  the  ear  to  one  end  of  a  long  stick  of  tim- 
ber, and  let  some  one  gently  scratch  the  other  end  with  a  pin. 

Experiment  4.  The  following  experiment  will  be  found  very  in- 
structive and  satisfactory  :  Let  two  persons  stand  about  fifteen  rods 
apart,  and  one  of  them  strike  two  pebble-stones  together,  so  as  to  be 
scarcely  audible  to  the  other.  Then,  when  at  the  same  distance  apart, 
let  one  of  them  dive  to  the  bottom  of  a  pond  of  water,  or  hold  one  ear 
for  a  few  seconds  beneath  the  surface  of  the  water,  while  the  other, 
extending  his  hands  into  the  water,  strikes  the  stones  together  as 
before.  The  sound  is  much  more  audible  than  when  conveyed  by  air. 

Solids  and  liquids,  as  well  as  gases,  transmit  sound-vibrations. 


284  SOUND. 

XL.   VELOCITY  OF  SOUND. 

§  263.  On  what  velocity  of  sound  depends.  —  The  flash 
of  a  gun,  however  distant,  is  seen  by  an  observer  at  the  instant 
it  is  made.  But  the  report,  if  the  distance  is  several  hundred 
yards,  is  heard  a  little  later.  If  the  distance  is  a  mile,  an  in- 
terval of  nearly  five  seconds  will  occur ;  so  that  sound  must 
occupy  that  time  in  traveling  a  mile,  or  it  must  travel  about 
1100  feet  in  a  second,  —  a  velocity  somewhat  less  than  that  of 
a  rifle  ball. 

It  is  apparent  that  sound  must  travel  more  slowly  in  a  dense 
than  in  a  rare  medium,  inasmuch  as  in  the  former  there  is  a 
greater  mass  to  be  moved ;  on  the  other  hand  (see  page  277), 
it  travels  faster  in  the  medium  that  is  the  most  elastic.  Density 
retards  and  elasticity  increases  the  velocity  of  sound.  The  rela- 
tion of  velocity  to  the  density  and  elasticity  of  gases,  as  ascer- 
tained by  careful  experiment,  is  as  follows  :  the  velocity  of  sound 
in  gases  is  directly  proportional  to  the  square  root  of  their  elasti- 
city, and  inversely  proportional  to  the  square  root  of  their 
respective  densities. 

The  velocity  of  sound  in  air  at  0°C.  has  been  found  to  be 
333m  (1093  ft.)  per  second.  Its  velocity  increases  nearly  six- 
tenths  of  a  meter  for  each  degree  centigrade.  At  the  temper- 
ature of  16°  C.  (60°  F.)  we  may  reckon  the  velocity  of  sound 
at  about  342m  (1125  ft.)  per  second. 

The  greater  density  of  solids  and  liquids,  as  compared  with 
gases,  tends,  of  course,  to  diminish  the  velocity  of  sound ;  but 
their  greater  elasticity1  more  than  compensates  for  the  decrease 
of  velocity  occasioned  by  the  increase  of  density.  As  a  general 
rule,  solids  are  more  elastic  than  liquids  ;  hence,  sound  generally 
travels  faster  in  the  former  than  in  the  latter.  For  example, 
sound  travels  in  water  about  4  times  as  fast  as  in  air ;  in  lead, 

1  The  question  will  very  pertinently  arise  here,  inasmuch  as  gases  are  (page  53)  per- 
fectly elastic,  How  can  solids  and  liquids  be  regarded  as  having  greater  elasticity?  It 
should  be  understood  that  while  gases  completely  recover  their  volume  after  a  compres- 
sing force  is  removed,  they  do  it  more  sluggishly  than  solids  and  liquids. 


REFLECTION.  285 

4  times ;  in  gold,  5  times ;  in  brass,  10  times  ;  in  copper,  11 
times ;  in  iron,  16  times ;  in  glass,  16  times  ;  in  wood,  along 
the  fiber,  between  10  and  15  times ;  in  wood,  across  the  fiber, 
between  4  and  6  times. 

QUESTIONS. 

1.  (a)  If  a  body  of  gas  is  compressed,  how  is  its  density  or  volume 
affected?    (See  page  156.)    (6)  How  is  its  elasticity  affected?    (c)  How 
is  it  affected  as  regards  the  velocity  with  which  it  will  transmit  sound? 

2.  Hydrogen  is  sixteen  times  lighter  (or  rarer)  than  oxygen  under 
the  same  pressure,     (a)  In  which  will  sound  travel  faster?     (6)  Why? 
(c)  How  many  times  faster? 

3.  When  sound  travels  in  air  with  a  velocity  of  33 lm  per  second,  it 
travels  in  carbonic  acid  gas  at  the  rate  of  262m  per  second,    (a)  Which 
is  the  denser  gas?     (6)  How  many  times  denser? 

4.  When  a  confined  body  of  air  is  heated,  it  has  its  elasticity  in- 
creased without  any  change  of  density.     How  will  this  affect  transmis- 
sion of  sound? 

5.  If  air  is  heated  and  allowed  to  expand  freely,  as  on  a  warm 
summer  day,  its  elasticity  is  unaffected,  but  its  density  is  diminished ; 
how  will  this  affect  the  transmission  of  sound? 


XLI.  KEFLECTION  AND  REFRACTION  OF  SOUND. 

§  264.  Reflection.  —  In  the  experiment  with  the  spiral 
spring,  waves  were  reflected  from  the  box  to  the  hand,  and 
from  the  hand  to  the  box.  When  a  sound-wave  meets  an 
obstacle  in  its  course,  it  is  reflected ;  and 'a  sound  heard  after 
being  thus  reflected  is  often  called  an  ec/io,  or  reverberation  when 
many  times  reflected,  so  that  the  sound  becomes  nearly  con- 
tinuous. 

§  265.  Sound  reflected  by  concave  mirrors.  —  Experi- 
ment. Place  a  watch  at  the  focus  (page  286)  A,  Figure  208,  of  a  con- 
cave mirror  G.  At  the  focus  B  of  another  concave  mirror  H,  place  the 
large  opening  of  a  small  tunnel,  and  with  a  rubber  connector  attach 
the  bent  glass  tube  C  to  the  nose  of  the  tunnel.  The  extremity  D 
being  placed  in  the  ear,  the  ticking  of  the  watch  can  be  heard  very 


286  SOUND. 

distinctly,  as  though  it  were  somewhere  near  the  mirror  H.  Though 
the  mirrors  be  5m  apart,  the  sound  will  be  heard  much  louder  at  B  than 
at  an  intertermediate  point  E. 

How  is  this  explained?  Every  air-particle  in  a  certain 
radial  line,  as  Ac,  receives  and  transmits  motion  in  the  direc- 
tion of  this  line ;  the  last  particle  strikes  the  mirror  at  c,  and 
being  perfectly  elastic,  bounds  off  in  the  direction  cc'  in  con- 
formity to  the  law  of  reflection  (page  118),  communicating  its 
motion  to  the  particles  in  this  line.  At  c'  a  similar  reflection 
gives  motion  to  the  air-particles  in  the  line  c'B.  In  consequence 
of  these  two  reflections,  all  divergent  lines  of  force,  as  Ad,  Ae, 

etc.,  that  meet  the  mirror 

Fig-208'  G,    are    there     rendered 

parallel,  and  afterwards 
rendered  convergent  at 
the  mirror  H.  The  prac- 
tical result  of  the  concen- 
tration of  this  scattering 
force  is,  that  a  sound  of 
great  intensity  is  heard  at  B.  The  points  A  and  B  are  called 
the  foci  of  the  mirrors.  The  front  of  the  wave  as  it  leaves  A 
is  convex,  in  passing  from  G  to  H  it  is  plane,  and  from  H 
to  B  concave.  If  you  fill  a  large  circular  tin  basin  with 
water,  and  strike  one  edge  with  a  knuckle,  circular  waves  with 
concave  fronts  will  close  in  on  the  center,  heaping  up  the 
water  at  that  point. 

Long  "whispering-galleries"  have  been  constructed  on  this  prin- 
ciple. Persons  stationed  at  the  foci  of  the  concave  ends  of  the  long 
gallery  can  carry  on  a  conversation  in  a  whisper  which  persons  be- 
tween cannot  hear.  A  most  notable  instance  was  that  of  the  "  Ear  of 
Dionysius,"  in  the  dungeon  of  Syracuse.  The  roof  of  the  prison  was 
so  constructed  as  to  transmit  through  a  narrow  passage  cut  in  the  rock, 
to  the  ear  of  the  tyrant,  even  the  whispers  of  the  victims  there  con- 
fined. 

The  external  ear  is  a  sound  condenser.  The  hand  held  concave 
behind  the  ear,  by  its  increased  surface,  adds  to  its  efficiency.  An  ear- 


REFRACTION.  287 

trumpet,  by  successive  reflections,  serves  to  concentrate,  at  the  small 
orifice  opening  into  the  ear,  all  the  sound-waves  that  enter  at  the  large 
end. 

§  266.  Refraction.  —  If  you  place  your  ear  at  the  small  end 
of  a  tunnel  C  (Fig.  209),  and  listen  to  the  ticking  of  a  watch  A, 


Fig.  209. 


4m  distant,  and  then  introduce  a  collodion  balloon  B  filled  with 
carbonic  acid  gas  between  your  ear  and  the  watch,  and  very 
near  the  latter,  the  sound  becomes  much  louder. 

The  cause  is  obvious ;  for,  let  the  curved  lines  «,  6,  c,  etc.,  represent 
sections  of  sound-waves  with  convex  fronts,  and  B  a  spherical  body 
of  carbonic  acid  gas  which  is  denser  than  air ;  then  it  is  clear  that, 
owing  to  the  slower  progress  of  the  waves  in  the  denser  gas,  they 
would  become  flattened  on  entering  this  gas,  and  the  waves  of  convex 
fronts  may  be  changed  to  waves  of  plane  fronts.  Again,  points  at 
the  extremities  of  the  waves,  having  less  distance  to  travel  in  the  denser 
gas  than  points  near  the  center,  would  emerge  first  and  get  in  advance, 
and  thus  the  wave  fronts  which  are  plane  while  wholly  in  the  dense 
gas,  become  concave  on  leaving  it.  By  these  changes  in  the  form  of 
the  wave  fronts,  sound  energy  which  was  originally  becoming  diffused 
through  wider  and  wider  space,  and  therefore  becoming  less  intense 
as  it  progressed,  is  so  changed  in  direction  in  passing  into  and  out  of 
a  medium  of  greater  density,  that  the  energy  is  finally  concentrated  at 
a  distant  point,  as  at  C,  and  thereby  intensified. 

Any  change  in  direction  of  sound,  caused  by  passing  from  a 
medium  of  a  certain  density  into  a  medium  of  different  density, 
is  called  refraction. 


288  SOUND. 


XLII.    LOUDNESS   OF   SOUND. 

§  267.  Loudness  depends  on  amplitude  of  vibrations.  — 
Gently  tap  the  prongs  of  a  tuning-fork  and  dip  them  into  water, 
—  the  water  is  scarcely  moved  by  them  ;  increase  the  force  of 
the  blow, — the  vibrations  become  wider,  and  the  water  spray  is 
thrown  with  greater  force  and  to  a  greater  distance.  The  same 
thing  occurs  when  the  fork  vibrates  in  air ;  though  we  do  not 
see  the  air-particles  as  they  are  batted  by  the  moving  fork, 
yet  we  feel  the  effects  as  a  sound  sensation,  and  we  judge  of 
their  energy  by  the  intensity  of  the  sensation.  Loudness  of 
sound  is  really  the  measure  of  a  sensation  ;  but  as  we  have  no 
suitable  or  constant  standard  of  measurement  for  a  sensation, 
we  are  compelled  to  measure  ratheV  the  intensity  of  the  sound- 
wave, knowing  at  the  same  time  that  the  loudness  is  not  pro- 
portional to  this  intensity  ;  unfortunately  the  expressions  loud- 
ness  and  intensity  of  sound  are  often  interchanged.  The  inten- 
sity m  of  a  vibration  is  measured  by  the  energy  of  the  vibrating 
particle.  It  is  clear  that  if  the  amplitude  of  vibration  of  a 
particle  is  doubled  while  its  period  remains  constant,  its  velocity 
is  doubled  (or  nearly  so) ,  and  its  energy  becomes  therefore  four 
times  as  much  as  at  first.  Hence,  (1)  Measured  mechanically, 
the  loudness  or  intensity  of  sound  is  proportional  to  the  square 
of  the  amplitude  of  the  vibrations  of  the  sounding  body. 

§  268.  Loudness  depends  upon  the  density  of  the  me- 
dium. —  In  the  experiment  with  the  watch  under  the  receiver 
of  the  air-pump  (page  281),  the  sound  grew  feebler  as  the  air 
became  rarer.  Aeronauts  are  obliged  to  exert  themselves 
more  to  make  their  conversation  heard  when  they  reach  great 
hights  than  when  in  the  denser  lower  air.  Fill  a  glass  bell- jar 
with  hydrogen  gas,  and  place  in  it  a  small  alarm  clock ;  the 
sound  is  exceedingly  weak  and  thin,  as  compared  with  the 
sound  when  the  jar  is  filled  with  air.  These  experiments  teach 
us,  (2)  that  the  intensity  of  sound  depends  upon  the  density  of 


LOUDNESS   DEPENDS   ON  DISTANCE.  289 

the  medium  in  which  it  is  produced.  In  a  rare  medium  a  vibrat- 
ing body  during  a  single  vibration  sets  in  motion  either  fewer 
particles,  as  in  the  case  of  the  partially  exhausted  receiver,  or, 
as  in  the  case  of  the  hydrogen  gas,  it  sets  in  motion  lighter  par- 
ticles than  in  a  dense  medium ;  consequently  it  parts  with  its 
energy  more  slowly,  and  the  sound  is  consequently  weaker. 

(In  which  ought  the  vibrations  of  a  body  to  last  longer,  —  in 
a  dense  or  in  a  rare  medium  ?  Why  ?) 

§  269.  Loudness  depends  on  distance.  —  It  is  a  matter 
of  every-day  observation  that  the  loudness  of  a  sound  dimin- 
ishes very  rapidly  as  the  distance  from  its  source  to  the  ear 
increases.  The  ear  is  not,  however,  able  to  compare  very  accu- 
rately the  loudness  of  two  sounds ;  for  instance,  it  cannot 
determine  when  one  sound  is  just  twice  as  loud  as  another. 
This,  however,  so  far  as  it  is  affected  by  distance,  can  be  very 
accurately  determined  by  calculation.  For  it  is  evident  that  as 
a  sound-wave  recedes  from  its  source  in  an  ever- widening  sphere, 
a  given  amount  of  energy  becomes  distributed  over  an  ever- 
increasing  surface ;  and  as  a  greater  number  of  particles  par- 
take of  the  motion,  individual  particles  receive  proportionally 
less  energy  ;  hence  it  follows,  —  as  a  consequence  of  the  geomet- 
rical truth,  that  the  surface  of  a  sphere  varies  as  the  square  of  its 
radius,  —  that  (3)  the  intensity  of  sound  varies  inversely  as  the 
square  of  the  distance  from  its  source.  For  example,  if  two  per- 
sons, A  and  B,  are  respectively  500  and  100D  meters  from  a  gun 
when  it  is  discharged,  the  report  that  reaches  A  will  be  four 
times  as  loud  as  the  same  report  when  it  reaches  B. 

§  270.  Speaking  tubes.  —  Experiment.  Place  a  watch  at  one 
end  of  the  long  tin  tube  (Fig.  206) ,  and  the  ear  at  the  other  end.  The 
ticking  is  heard  very  loud,  as  though  the  watch  were  close  to  the  ear. 

Long  tin  tubes,  called  speaking  tubes,  passing  through  many 
apartments  in  a  building,  enable  persons  at  the  distant  extremi- 
ties to  carry  on  conversation  in  a  low  tone  of  voice,  while  per- 


290  SOUND. 

sons  in  the  various  rooms  through  which  the  tube  passes  hear 
nothing.  The  reason  is  that  the  sound-waves  which  enter  the 
tube  are  prevented  from  expanding,  consequently  the  intensity 
of  sound  is  not  affected  by  distance,  except  as  its  energy  is 
wasted  by  friction  of  the  air  against  the  sides  of  the  tube. 

§  271.  Keenforcement  of  sound.  —  Observe  the  difference 
.between  the  loudness  of  a  sound  made  in  a  room,  and  the  same 
made  in  the  open  air.  In  a  room  of  moderate  size  the  original 
and  reflected  sounds  are  heard  simultaneously,  one  intensifying 
the  other  and  producing  what  is  called  resonance.  In  large 
rooms,  the  blending  of  the  two  is  not  perfect,  resulting  in  a  sort 
of  blurred  sound,  which  is  loud  but  indistinct. 

Experiment.  Set  a  tuning-fork  in  vibration ;  you  can  scarcely  hear 
the  sound  produced  unless  it  is  held  near  the  ear.  Press  the  stem 
against  a  table ;  the  sound  rings  out  loud,  but  seems  to  proceed  from 
the  table.  Again  set  it  vibrating,  hold  it  to  the  ear,  and,  watch  in 
hand,  note  the  number  of  seconds  it  can  be  heard ;  then  note  the  time 
that  it  can  be  heard  when  the  stem  rests  on  the  table.  The  vibrations 
continue  longer  in  the  former  case  than  in  the  latter. 

"When  only  the  fork  vibrates,  the  prongs  presenting  little  sur- 
face cut  their  way  through  the  air,  producing  very  slight  conden- 
sations, and  consequently  sounds  of  little  intensity.  When  the 
fork  rests  upon  the  table,  the  vibrations  are  communicated  to 
the  table  ;  the  table  with  its  larger  surface  throws  a  larger  mass 
of  air  into  vibration,  and  thus  greatly  intensifies  the  sound. 
But  as  the  sound  is  rendered  more  intense,  the  energy  of  the 
vibrating  body  is  sooner  exhausted,  and  the  sounds  have  shorter 
duration. 

In  all  stringed  instruments,  like  the  piano,  violin,  etc.,  ree'ii- 
forcement  of  sound  is  necessary ;  here  the  sounding  board  or 
thin  wood  fills  more  perfectly  the  place  of  the  table.  This 
sounding  board  must  strengthen  all  notes  within  the  compass  of 
the  instrument.  The  strings  of  the  piano,  guitar,  and  violin 
owe  as  much  of  their  loudness  of  sound  to  their  elastic  sounding 
boards,  as  does  the  fork  to  the  table. 


REENFOKCEMENT   BY   MASSES   OF   AIE. 


291 


§  272.  Reenforcement  by  masses  of  air.  —  Resonators. 
—  Experiment.  Take  a  glass  tube  A,  Figure  210,  45cm  long  and  4cm 
in  diameter ;  thrust  one  end  into  a  vessel  of  water,  C,  and  hold  over  the 
other  end  a  vibrating  tuning-fork  B  that  makes  (say)  256  vibrations  in 
a  second.  (See  page  300.)  Gradually  lower  the  tube  into  the  water, 
and  when  it  reaches  a  certain  depth,  i.e.,  when  the  column  of  air  oc 
attains  a  certain  length,  the  sound 


of  the  fork  becomes  very  loud ; 
continuing  to  lower  the  tube,  the 
sound  rapidly  dies  away.  Try 
other  forks  that  make  different 
numbers  of  vibrations  in  a  sec- 
ond. The  sound  of  each  is  inten- 
sified, but  each  requires  a  length 
of  air-column  suited  to  its  par- 
ticular vibration  number. 


Fig.  210. 


...  C 


Columns  of  air  are  thus 
found  to  serve  as  well  as 
sounding  boards  to  strengthen 
a  sound.  When  so  used  they 
are  called  resonators;  but  unlike  the  sounding  board  they  can 
respond  loudly  to  only  one  tone,  or  to  a  few  tones  of  widely 
different  pitch.  An  important  form  of  resonator  is  shown  on 
page  309. 

How  is  this  reenforcement  effected  ?  When  the  prong  a  moves 
from  one  extremity  of  its  arc  a'  to  the  other  a",  it  sends  a  con- 
densation down  the  tube  ;  this  condensation*  striking  the  surface 
of  the  water,  is  reflected  by  it  up  the  tube.  Now  suppose  that 
the  front  of  this  reflected  condensation  should  just  reach  the 
prong  at  the  instant  it  is  starting  on  its  retreat  from  a"  to  a' ; 
then  the  reflected  condensation  will  conspire  with  the  condensa- 
tion formed  by  the  prong  in  its  retreat  to  make  a  greater  con- 
densation in  the  air  outside  the  tube.  Again  the  retreat  of  the 
prong  from  a"  to  a'  produces  in  its  rear  a  rarefaction,  which  also 
runs  down  the  tube,  is  reflected,  and  will  reach  the  prong  at  the 
instant  it  is  about  to  return  from  a'  to  a",  and  to  cause  a  rare- 


292  SOUND. 

faction  in  its  rear ;  these  two  rarefactions  moving  in  the  same 
direction  conspire  to  produce  an  intensified  rarefaction.  The 
original  sounds  thus  combine  with  their  echoes  to  produce  reso- 
nance ;  but  this  can  only  happen  when  the  like  parts  of  each 
wave  coincide  each  with  each ;  for  if  the  tube  were  somewhat 
longer  or  shorter  than  it  is,  it  is  plain  that  condensations  would 
meet  rarefactions  in  the  tube,  and  tend  to  destroy  one  another. 
The  loudness  of  sound  of  all  wind  instruments  is  due  to  the 
resonance  of  the  air  contained  within  them.  A  simple  vibra- 
tory movement  at  the  mouth  or  orifice  of  the  instrument, 
scarcely  audible  in  itself,  such  as  the  vibration  of  a  reed  in  reed 
pipes,  or  a  pulsatory  movement  of  the  air  produced  by  the  pas- 
sage of  a  thin  sheet  of  air  over  a  sharp  wooden  or  metallic  edge, 
as  in  organ  pipes,  flutes,  and  flageolets,  or  more  simply  still 
by  the  friction  of  a  gentle  stream  of  breath  from  the  lips  sent 
obliquely  across  the  open  end  of  a  closed  tube,  bottle,  or  pen- 
Fig.  211.  case,  is  sufficient  to  set  the  large  body  of  enclosed 
air  in  the  instrument  into  vibration,  and  thus  ree'n- 
forced,  the  sound  becomes  audible  at  long  distances. 

Experiment  2.  Attach  a  rose  gas-burner  A,  Figure 
211,  to  a  metal  gas  tube  about  lm  in  length,  and  connect 
this  by  a  rubber  tube  with  a  gas-burner.  Light  the  gas 
at  the  rose  burner,  and  you  will  hear  a  low  rustling 
noise.  Remove  the  conical  cap  from  the  long  tin  tube 
(Fig.  206,  page  278),  support  the  tube  in  a  vertical  po- 
sition, and  gradually  raise  the  burner  into  the  tube; 
when  it  reaches  a  certain  point  not  far  up,  the  body  of 
air  in  the  tube  will  catch  up  the  vibrations,  and  give  out 
a  deafening  sound  that  will  shake  the  walls  and  furni- 
ture in  the  room. 


f 


§  273.  Measuring  wave-lengths  and  veloc- 
ity of  sound.  —  Experiments  like  that  described 
on  page  291  enable  us  readily  to  measure  the  wave-length 
produced  by  a  fork  that  makes  a  given  number  of  vibrations 
in  a  second,  and  also  to  measure  the  velocity  of  sound.  It  is 


MEASURING    VELOCITY  -OF    SOUND.  293 

evident  that  if  a  condensation  generated  by  the  prong  of  the 
fork  in  its  forward  movement  from  a1  to  a"  (Fig.  211)  met 
with  no  obstacle,  its  front,  meantime,  would  traverse  the  dis- 
tance od,  or  twice  the  distance  oc ;  hence  the  length  of  the  con- 
densation is  the  distance  od.  But  a  condensation  is  only  one- 
half  of  a  wave,  and  the  passage  of  the  prong  from  a'  to  a"  is 
only  one-half  of  a  vibration  ;  consequently  the  distance  od  is 
one-half  of  a  wave-length,  and  the  distance  oc  is  one-fourth 
of  a  wave-length.  The  measured  distance  of  oc  in  this  case  is 
about  33cm ;  hence  the  length  of  wave  produced  by  a  C'-fork 
making  256  vibrations  in  a  second  is  (33cm  x4  =)  1.32™.  And 
since  a  wave  from  this  fork  travels  1.32™  in  Y^-g  of  a  second, 
it  will  travel  in  an  entire  second  (1.32  x  256  =  )  338m.  The 
distance  oc  is  modified  by  temperature.  It  is  also  modified  by 
the  diameter  of  the  tube.  For  accuracy  about  two-thirds  of  the 
diameter  should  be  added  to  the  length  of  the  tube  to  obtain 
one-fourth  of  the  wave-length.  It  is  evident  that  the  three 
quantities  expressed  in  the  formula 

wave-length  = ^ 

number  of  vibrations 

bear  such  a  relation  to  one  another  that  if  any  two  are  known 
the  remaining  quantity  can  be  computed.  It  will  further  be 
observed  that  with  a  given  velocity  the  ivave-length  varies 
inversely  as  the  number  of  vibrations,  i.e.,  the  greater  the  num- 
ber of  vibrations  per  second,  the  shorter  the,  wave-length. 

QUESTIONS. 

1.  (a)  Which  produces   greater  wave-lengths,   a  fork  making  25G 
vibrations  in  a  second,  or  one  making  512  vibrations  in  the  same  time? 
(ft)  How  many  times? 

2.  Disregarding  the  diameter  of  the  tube,  what  number  of  vibrations 
does  a  fork  make  in  a  second,  whose  resonance  tube  is  22.26cm  long, 
when  the  temperature  is  16°  C.  ? 

3.  What  is  the  wave-length  produced  by  a  fork  that  makes  384  vibra- 
tions in  a  second,  when  the  temperature  is  16°  C.? 


294 


SOUND. 


§  274.  Interference  of  sound-waves.  —  Is  it  possible  for 
two  sounds  to  destroy  one  another  and  produce  silence  ? 

Fig.  212.  Experiment  1.  While  the  fork 

B  (Fig.  210)  is  vibrating  in  the 
position  represented  in  the  figure, 
slowly  roll  the  fork  over  in  the 
fingers,  through  a  quarter  of  a 
revolution,  until  the  two  prongs 
are  in  the  same  horizontal  plane, 
with  their  edges  turned  toward 
the  opening  of  the  tube.  When 
the  fork  has  accomplished  one- 
eighth  of  a  revolution,  and  is  in 
an  oblique  position,  as  in  Figure 
212,  the  reenforcement  from  the 
tube  entirely  disappears,  but  re- 
appears when  the  fork  completes 

its  quarter  of  a  revolution.  Return  to  the  position  where  there  is  110 
resonance,  and  enclose  the  prong  farthest  from  the  tube,  without  touch- 
ing the  fork,  in  a  loose  roll  of  paper,  so  as  to  prevent  the  sound- 
waves produced  by  that  prong  from  passing  into  the  tube;  the 
resonance  resulting  from  the  vibrations  of  the  other  prong  immediately 
appears  in  full  force. 

Experiment  2.  Carry,  while  sounding,  a  tuning-fork  mounted  on 
a  resonance-box  (see  Fig.  214),  from  a  distance  slowly  toward  a  wall 
of  a  room ;  the  sound  will  become  wavy,  rising  and  sinking  at  regu- 
lar intervals.  That  is,  at  certain  points  the  condensations  and  rare- 
factions of  the  waves  advancing  from  the  fork  will  coincide  each  to 
each  with  those  of  the  waves  reflected  from  the  wall,  and  when  this  is 
the  case  the  sound  is  louder.  At  other  points  the  condensations  of  the 
waves  issuing  from  the  fork  occur  at  the  same  places  where  the  rare- 
factious  of  the  reflected  waves  occur;  and  in  this  case  they  nearly 
destroy  one  another,  and  a  fainter  sound  is  the  result. 

Thus  it  appears  that  two  sounds  of  the  same  pitch  may  unite 
to  form  a  sound  louder  or  weaker  than  either  alone,  or  even 
cause  silence,  according  to  their  difference  of  phase  and  their  rela- 
tive intensities.  When  like  phases  of  two  sets  of  sound-waves 
coincide,  i.e.,  condensation  with  condensation,  and  rarefaction 


FORCED   AND   SYMPATHETIC   VIBRATIONS. 


295 


with  rarefaction,  the  result  is,  as  we  might  expect,  an  intensified 
sound.  In  this  case  the  air-particles  are  subject  to  the  action 
of  two  joint  forces  in  the  same  direction,  which  tends  to  quicken 
their  motions.  On  the  other  hand,  when  unlike  phases  of  two 
sets  of  sound-waves  coincide,  i.e.,  the  condensations  of  one  set  of 
waves  with  the  rarefactions  of  another,  as  would  happen  if  one 
set  of  waves  should  be  half  of  a  wave-length  behind  the  other  ; 
the  air-particles  will  be  subject  to  two  forces  in  opposite  direc- 
tions ;  and  the  evident  result  of  an  equal  tendency  to  the  two 
opposing  forces  is  a  state  of  repose. 


Fig.  213. 


§275.  Forced  and  sympathetic  vibrations. —Experi- 
ment 1.  Suspend  by  a  string  lm  long  a  stone  weighing  about  2k. 
Swing  the  stone,  and  learn  its  rate  of  vibration ;  then  stop  it,  and  blow 
gentle  puffs  of  breath  against  the  stone  in  the  same  periods.  The  first 
few  puffs  produce  no  visible  effect;  but,  persevering,  the  stone  will 
soon  move  visibly,  and  after  a  large  number 
of  these  feeble  impulses,  the  stone  will  move 
through  a  wide  arc,  and  will  require  consid~ 
erable  force  to  stop  it. 

Experiment  2.  Suspend  from  a  frame 
several  pendulums,  A,  B,  C,  etc.  (Fig.  213). 
A  and  D  are  each  lm  long,  C  a  little  longer, 
and  B  and  E  shorter.  Set  A  in  vibration,  and 
slight  impulses  will  be  communicated  through 
the  frame  to  D  and  cause  it  to  vibrate.  The 
vibration-period  of  D  being  the  same  as  that 
of  A,  all  the  impulses  tend  to  accumulate  mo- 
tion in  D,  so  that  it  soon  vibrates  through 
arcs  as  large  as  those  of  A.  On  the  other  hand,  C,  B,  and  E,  having 
different  rates  of  vibration  from  that  of  A,  will  at  first  acquire  a  slight 
motion,  but  soon  their  vibrations  will  be  in  opposition  to  those  of  A, 
and  then  the  impulses  received  from  A  will  tend  to  destroy  the  slight 
motion  they  had  previously  acquired. 

Experiment  3.  Hang  up,  a  few  feet  distant  from  the  pendulum  of 
Exp.  1,  a  bullet  or  shot  by  a  shorter  string,  and  connect  the  bullet  and 
stone  by  a  tight  thread.  Set  the  stone  swinging,  and  the  bullet  must 
vibrate  in  the  same  period,  although  its  natural  time  of  vibration  is 
shorter. 


296 


SOUND. 


Fig.  214. 


Experiment  4.  Press  down  gently  one  of  the  keys  of  a  piano  so  as 
to  raise  the  damper  without  making  any  sound,  and  then  sing  loudly 
into  the  instrument  the  corresponding  note.  The  string  correspond- 
ing to  this  note  will  be  thrown  into  vibrations  that  can  be  heard  for 
several  seconds  after  the  voice  ceases.  If  another  note  be  sung,  this 
string  will  not  respond  audibly. 

Raise  the  dampers  from  all  the  strings  of  the  piano  by  pressing  the 
foot  on  the  right-hand  pedal,  and  sing  strongly  some  note  into  the 
piano.  Although  all  the  strings  are  free  to  vibrate,  only  those  that 
correspond  to  the  note  you  sing  (i.e.,  those  that  are  capable  of  making 
the  same  number  of  vibrations  per  second  as  are  produced  by  your 
voice) ,  will  respond  loudly. 

Experiment  5.  Take  two  forks,  A  and  B  (Fig.  214),  tuned  exactly 
in  unison,  and  mounted  on  resonance-boxes,  and  place  them  from  three 

to  ten  meters  apart.  Fasten, 
by  a  bit  of  sealing-wax,  a 
thread  to  a  thin  piece  of  glass 
12mm  square  (glass  used  for  mi- 
croscopic mountings  is  the 
best,  or  a  piece  of  photographic 
tintype  plate  will  answer  well), 
and  suspend  so  as  to  touch  a 
corner  of  one  of  the  prongs  of 
the  fork  B.  Set  the  fork  A  in 
vibration  by  drawing  a  resined  bass-viol  bow  strongly  across  the  ends 
of  its  prongs.  In  about  ten  seconds  stop  the  vibrations  of  A  with  the 
fingers,  and  you  will  see  and  hear  the  piece  of  glass  rattling  against 
the  prong  of  the  fork  B ;  remove  the  glass,  and  place  the  ear  near  the 
fork  B,  or  better,  the  open  end  of  the  box,  and  you  may  hear  a  distinct 
sound,  showing  that  the  fork  B  has  been  thrown  into  a  state  of  vibra- 
tion by  the  fork  A. 

So  the  pulses  that  traverse  the  air  between  the  forks,  so 
gentle  that  only  the  sensitive  organ  of  the  ear  can  perceive 
them,  become  great  enough  to  move  the  rigid  steel  when  their 
blows,  dealt  at  the  rate  of  perhaps  512  in  a  second,  add  them- 
selves together.  The  large  number  of  blows  make  up  for  the 
feebleness  of  each  by  itself. 

These  experiments  show  that  a  vibrating  body  tends  to  make 
other  bodies  near  it  vibrate  in  its  own  period.  The  vibrations 


DISTINCT! OK   BETWEEN   NOISE  AND   MUSIC.          297 

thus  caused  are  called  forced  vibrations.  These  occur,  in  Exp.  2, 
with  B,  C,  and  E ;  in  the  vibrations  of  sounding-boards,  and 
of  the  membrane  and  fluids  of  the  ear  (page  315),  and  in  the 
air  when  transmitting  a  sound-wave,  etc.  But  as  the  period  of 
the  incident  waves  coincides  more  and  more  nearly  with  the 
period  of  the  second  body,  the  amplitude  of  the  vibrations  of 
the  latter  becomes  greater  and  greater,  until  finally  its  vibration 
is  uniform,  like  D  (Fig.  213),  not  irregular,  like  B,  C,  and  E. 
Such  are  called  sympathetic  vibrations,  as  in  Exps.  4  and  5. 

§  276.  Distinction  between  noise  and  musical  sound. 
If  the  body  that  strikes  the  air  deals  it  but  a  single  blow,  like  the 
discharge  of  a  fire-cracker,  the  ear  receives  but  a  single  shock, 
and  the  result  is  called  a  noise.  If  several  shocks  are  slowly 
received  by  the  ear  in  succession,  the  ear  distinguishes  them 
as  so  many  separate  noises.  If,  however,  the  body  that  strikes 
the  air  is  in  vibration,  and  deals  it  a  great  number  of  little  blows 
in  a  second,  or  if  a  large  number  of  fire-crackers  are  discharged 
one  after  another  very  rapidly,  so  that  the  ear  is  unable  to  dis- 
tinguish the  individual  shocks,  the  effect  produced  is  that  of  one 
continuous  sound,  which  may  be  pleasing  to  the  ear  ;  and,  if  so, 
it  is  called  a  musical  sound.  But  continuity  of  sound  does  not 
necessarily  render  it  musical.  The  sound  produced  by  a  hun- 
dred children  beating  various  articles  in  a  room  with  clubs 
might  not  be  lacking  in  continuity,  but  it  would  be  an  intoler- 
able noise.  There  would  be  wanting  those  elements  that  please 
the  ear ;  viz.,  regularity  both  in  periodicity  and  intensity  of  the 
shocks  which  it  receives.  The  distinction  between  music  and 
noise  is,  generally  speaking,  a  distinction  between  the  agreeable 
and  the  disagreeable,  between  regularity  and  confusion.  The 
characteristics  of  a  musical  sound  are  regularity  and  simplicity. 


298 


SOUND. 


Fig.  215. 


XLIII.     PITCH    OF    SOUNDS. 

§  277.  On  what  pitch  depends.  —  Draw  the  finger-nail 
slowly,  and  then  rapidly,  across  the  teeth  of  a  comb.  The  two 
musical  sounds  produced  are  commonly  described  as  low  or 
grave,  and  high  or  acute,  and  the  hight  of  a  musical  sound  is 
called  pitch.  What  is  the  cause  of  a  difference  in  hight  or 
pitch  of  two  sounds? 

Experiment.  Procure  a  circular  sheet-iron  or  pasteboard  disk  A, 
Figure  215,  30cm  in  diameter.  From  the  center  of  the  disk  describe  a 
circle  with  a  radius  of  12cm.  In  the  circumfer- 
ence of  this  circle,  with  a  punch,  cut  holes  8mm 
in  diameter,  leaving  equal  intervals  of  about  2cm 
between  the  holes.  Insert  in  a  rubber  tube  a 
piece  of  glass  tube  B,  of  lcra  bore,  drawn  out  at 
one  end  so  that  its  orifice  is  about  4mm  in  diame- 
ter. Attach  the  disk  to  some  rotating  apparatus, 
hold  the  small  orifice  of  the  glass  tube  opposite 
the  holes,  and  blow  steadily  through  the  tube, 
and  rotate  the  disk  at  first  very  slowly  and  then 
with  gradually  increasing  rapidity.  The  breath, 
as  it  makes  its  exit  from  the  tube,  cannot  escape 
continuously  through  the  holes,  but  is  cut  up  by 
the  passing  obstructions  into  a  series  of  puffs, 
which  at  first  are  heard  as  so  many  distinct 
sounds ;  as  the  speed  increases,  the  number  of 
puffs  in  a  second  increases,  until  the  ear  can  no 
longer  separate  them,  when  they  blend  together 
in  a  deep  sound  of  a  definite  pitch. 

The  peculiarity  of  this  instrument  is  that  it  does  not  produce 
sound  by  its  own  vibrations.  Every  time  the  air  is  driven 
through  a  hole,  it  produces  a  pulse  of  condensation  in  the  air 
beyond ;  and  during  the  interval  between  the  successive  dis- 
charges, a  pulse  of  rarefaction  will  be  caused  by  the  elasticity  of 
the  air,  so  that  the  result  is  the  same,  so  far  as  the  effect  on 
the  air  medium  is  concerned,  as  if  a  body  were  vibrating 
in  it.  As  the  velocity  increases,  the  pitch  constantly  rises, 


SIREN.  299 

until,  at  the  greatest  speed  conveniently  attainable,  it  becomes 
painfully  shrill.  Varying  the  force  of  the  breath  affects  the 
loudness  of  the  sound,  but  does  not  affect  its  pitch. 

We  learned  on  page  293  that  on  the  number  of  vibrations  in 
a  second,  called  the  vibration-frequency,  depends  the  wave- 
length. So  we  have  discovered  the  important  fact  that  pitch 
depends  upon  vibration-frequency  or  wave-length,  i.e.,  the  greater 
the  number  of  vibrations  per  second,  or  the  shorter  the  wave- 
length, the  higher  the  pitch. 

QUESTIONS  AND   EXERCISES. 

1.  Why  does  the  same  bell  always  give  a  sound  of  the  same  pitch? 

2.  (a)  What  is  the  effect  of  striking  a  bell  with  different  degrees  of 
force?     (6)  What  change  in  the  vibrations  is  produced?     (c)  What 
property  of  sound  remains  the  same? 

3.  (a)  Strike  a  key  of  a  piano  and  hold  it  down ;  what  is  the  only 
change  you  observe  in  the  sound  produced  while  it  remains  audible? 
(&)  What  is  the  cause  of  this  change? 

4.  Rake  the  teeth  of  a  comb  with  a  finger-nail,  at  first  slowly,  then 
quickly,  and  account  for  the  difference  in  the  character  of  the  sounds 
produced. 

5.  (a)  On  what  does  pitch  depend?     (&)  On  what,  loudness? 

§  278.  How  to  find,  the  vibration-frequency  of  a  tone.  — 
Siren.  —  The  perforated  wheel  described  above  is  a  cheap 
imitation  of  a  portion  of  an  important  instrument  called  a  siren. 
The  instrument  completed  has  an  attachment  called  a  counter, 
which  shows  the  number  of  revolutions  the  wheel  makes  in  a 
given  time. 

Suppose  that  it  is  required  to  ascertain  the  number  of  vibra- 
tions per  second  necessary  to  produce  a  given  pitch.  Take 
some  instrument  that  gives  the  required  pitch,  e.g.,  a  tuning- 
fork,  set  it  in  vibration  ;  also  rotate  the  siren,  causing  the  pitch 
of  its  sound  gradually  to  rise  until  it  corresponds  with  the  pitch 
of  the  fork  ;  then,  sustaining  that  pitch,  set  the  counter  in  oper- 
ation, and  at  the  end  of  a  given  time  read  off  the  number  of 
revolutions  made  by  the  wheel ;  this  number,  multiplied  by  the 


300 


SOUND. 


number  of  holes  rn  the  wheel,  gives  the  numYn^  -of  sound- waves 
produced  by  the  wheel  during  the  given  time,  and  the  number 
of  vibrations  made  by  the  fork  in  the  same  time  ;  and  this  num- 
ber, divided  by  the  number  of  seconds  employed,  gives  the 
number  of  vibrations  that  must  be  made  in  a  second  by  any 
instrument  in  order  to  produce  a  sound  of  the  same  pitch. 
With  the  siren  we  may  even  determine  the  number  of  vibrations 
made  by  the  wing  of  a  fly  which  buzzes  ai  ound  our  ears. 


Fig.  216. 


§  279.  Musical  scale.  —  Long  before  a&y  one  had  attempted 
to  find  the  frequency  of  vibration  of  a  sounding  body,  men 
had  used  a  succession  of  sounds,  differing  in  pitch,  that 
formed  the  so-called  musical  scale,  or  gamut,  and  were  familiar 
with  its  intervals.  Very  different  scales  have  satisfied  musi- 
cians of  different  ages  and  nations.  We  can  find  a  scale  that 
will  nearly  or  exactly  satisfy  modern  musical  ears  among 
Europeans  and  Americans  on  a  well-tuned  piano  or  organ.  On 
such  a  piano,  by  the  siren  or  otherwise,  it  is  found  that  the  note 
called  middle  C  (C')  has,  on  the  'best  American 
instruments,  about  270  double  vibrations  per 
second ;  on  German,  264  ;  while  the  French 
legal  standard  is  261.  Physical  apparatus  is 
usually  based  on  C'=  256  vibrations,  256  being 
a  power  of  2.  Assuming  C'  =  264  vibrations, 
if  we  extend  our  measures  up  and  down  the 
scale,  or  get  a  violinist  or  singer  to  perform 
near  an  instrument  that  counts  the  vibrations, 
e.g.,  the  siren,  numbers  agreeing  very  closely 
with  those  given  in  Figure  216  are  obtained ; 
no  one's  ear  is  accurate  enough  to  play  or  sing 
precisely  the  same  on  two  trials.  Since  the  ear 
is  wholly  incapable  of  determining  the  number 
of  vibrations  corresponding  to  a  given  note, 
but  is  capable  of  determining  with  wondrous 
precision  the  ratio  of  the  vibration  numbers  of  two  notes,  it  is 


1 

jzj 

Vibration 
numbers. 

Vibration 
ratios. 

C 

132 

1 

D 

1481 

f 

E 

165 

F 

176 

4 

G 

198 

f 

A 

220 

B 

247  \ 

4 

C' 

264 

2 

D' 

297 

t 

E' 

330 

1 

F' 

352 

G' 

396 

3 

A' 

440 

B' 

495 

A 

C" 

528 

* 

LIMITS   OF   THE  SCALE  AND   HEARING.  301 

clear  that  all  music  must  depend  upon  the  recognition  of  such 
ratios.  For  this  reason  the  numbers  in  the  third  column  are  of 
great  importance.  The  eighth  note,  above  or  below  a  given 
note,  counting  the  given  note  as  one,  is  called  an  eighth,  —  more 
commonly,  an  octave,  —  above  or  below.  Thus  C'  is  the  octave 
above  C,  and  C—1  an  octave  below.  In  a  similar  manner  D  is 
called  the  second,  and  Gr  the  fifth,  etc.,  in  the  scale  in  which  C 
is  the  prime  or  first  note. 

PROBLEMS. 

1.  Find  the  vibration  number  for  each  note  of  the  scale  of  which 
C"  is  the  first  note. 

2.  What  is  the  vibration  number  of  C_i,  an  octave  below  C  ? 

3.  Find  the  wave-length  corresponding  to  each  note  of  the  scale  of 
which  C'  is  the  first,  when  the  temperature  of  the  air  is  16°  C.? 

4.  Find  the  length  of  a  resonance  tube  (disregarding  its  diameter), 
closed  at  one  end,  which  will  respond  to  C'  when  the  temperature  is 
16°  C.? 

§  280.  Limits  of  the  scale  and  hearing.  —  The  lowest 
note  of  a  7^  octave  piano  makes  about  27-J,  the  highest,  4,224 
vibrations  per  second  ;  but  these  extreme  notes  have  little  musical 
value,  and  the  lowest  notes  are  only  used  for  their  harmonics  (see 
page  305) .  The  range  of  the  human  voice  lies  between  100  and 
1,000  vibrations  per  second,  or  a  little  more  than  three  octaves ; 
an  ordinary  singer  has  about  the  compass  of  two  octaves. 

The  ear  is  capable  of  hearing  vibrations  far  exceeding  in  num- 
ber the  requirements  of  music.  It  can  appreciate  sounds  arising 
from  32  to  38,000  vibrations1  per  second,  i.e.,  a  range  of  about 
eleven  octaves,  and  a  corresponding  range  of  wave-length  be- 
tween seventy  feet  and  three  or  four-tenths  of  an  inch.  These 
numbers  vary,  however,  considerably  with  the  person.  Excep- 
tional ears  can  hear  as  many  as  50,000  vibrations.  Some  ears 
can  hear  a  bat's  cry,  or  the  creaking  of  a  cricket ;  others  cannot. 
Singing  mice  are  sometimes  placed  on  exhibition.  Of  those 
who  go  to  hear  them,  some  can  hear  nothing,  others  a  little,  and 

1  Preyer  places  the  lowest  limit  for  some  ears  at  16  vibrations  per  second. 


302  SOUND. 

others  again  can  hear  much.  In  the  ability  to  hear  sharp 
sounds,  no  animal  is  superior  to  the  cat,  which  finds  her  prey 
in  the  dark  by  its  squealing. 

§  281.  Beats.  —Experiment  1.  Strike  simultaneously  the  lowest 
note  of  a  piano  and  its  sharp  (black  key  next  above) ,  and  listen  to  the 
resulting  sound. 

Experiment  2.  Take  two  forks  which  make  the  same  number  of 
vibrations  per  second  (page  296),  load  one  of  the  prongs  of  one  fork 
by  sticking  to  it  a  small  ball  of  wax,  and  thereby  cause  it  to  make  a 
few  less  vibrations  per  second  than  the  other.  Set  both  forks  in  vibra- 
tion, and  note  the  result. 

In  both  cases  you  will  hear  a  peculiar  wavy  or  throbbing 
sound,  caused  by  an  alternate  rising  and  sinking  in  loudness. 
These  alternations  in  loudness  are  called  beats. 


Let  the  continuous  curve  line  A  C  (Fig.  217)  represent  a  series  of 
waves  proceeding  from  the  prongs  of  the  loaded  fork,  and  the  dotted 
line  a  series  of  waves  proceeding  from  the  other  fork.  As  explained 
on  page  311,  the  elevations  of  these  waves  may  represent  the  distance 
the  air-particle  has  been  moved  in  the  condensed  part  of  the  wave ; 
similarly  with  the  depressions  for  the  rarefied  part.  Now  the  waves 
from  both  forks  may  start  together  at  A ;  but  as  the  waves  from  the 
loaded  fork  are  given  less  frequently,  so  are  they  correspondingly 
longer  and  lag  behind;  and  at  certain  intervals,  as  at  B,  condensa- 
tions will  correspond  with  rarefactions,  producing  by  their  interference 
momentary  silence,  too  short,  however,  to  be  perceived ;  but  the  sound 
as  received  by  the  ear  is  correctly  represented  in  its  varying  loudness 
by  the  curved  line  in  the  lower  part  of  the  figure.  This  line  represents 
the  exact  resultant  of  the  two  alternately  concurring  and  opposing 
forces  on  the  particles  of  the  air  between  the  forks  and  the  ear. 


SONOMETER.  303 

If  one  of  the  forks  makes  256  vibrations,  and  the  other  255 
vibrations  in  a  second,  it  is  apparent  that  once  during  the  seo- 
ond  the  condensation  of  one  series  of  waves  will  coincide  with 
the  condensation  of  the  other,  producing  a  sound  of  maximum 
intensity ;  and  once  during  the  same  time  the  condensation  of 
the  one  will  coincide  with  the  rarefaction  of  the  other,  producing 
a  sound  of  minimum  intensity  ;  this  will  cause  just  one  beat  per 
second.  If  there  is  a  difference  of  two  vibrations  per  second 
between  the  two  forks,  then  there  will  be  two  beats  per  second. 

In  every  case  the  number  of  beats  per  second  due  to  two  simple 
tones  is  equal  to  the  difference  of  their  respective  vibration-num- 
bers. The  sensation  produced  on  the  ear  by  such  a  throbbing 
sound,  when  the  beats  are  sufficiently  frequent,  is  unpleasant, 
for  the  similar  reason  that  the  sensation  produced  by  flashes  of 
light  that  enter  the  eye,  when  3-011  walk  on  the  shady  side  of  a 
picket  fence,  is  unpleasant.  The  unpleasant  sensation,  called 
by  musicians  discord,  is  found  to  be  due  to  beats  (see  page 
307). 

XLIV.    VIBRATION   OF   STRINGS. 

§  282.  Sonometer.  —  Experiment.  Take  a  piece  of  violin-striDg 
or  piano-wire  a  little  longer  than  your  table.  Fasten  one  end  to  a 
nail  in  one  end  of  the  table,  Fig  218 

and  pass  the  other  end  over 
a  pulley  fastened  to  the 
other  end  of  the  table,  and 
to  this  end  of  the  string 
suspend  a  pail  containing 
sand,  the  two  weighing  just 
a  pound.  Place  under  the 
string,  near  the  ends  of  the 
table,  two  wedge-shaped 
bridges  A  and  B  (Fig.  218) .  An  apparatus  thus  arranged  is  called  a  so- 
nometer. Pluck  the  string  with  the  fingers  near  the  middle,  causing  it 
to  vibrate,  and  note  the  pitch  of  the  sound,  and  the  length  of  the  string 
between  the  bridges.  Move  the  bridge  A  toward  B ;  the  pitch  rises 
as  the  vibrating  portion  of  the  string  is  shortened.  Vary  the  position 
of  A  until  a  pitch  is  obtained  au  octave  above  the  pitch  given  at  first, 


304  SOUND. 

and  it  will  be  found  that  the  string  is  just  one-half  its  original  length ; 
i.e.,  by  halving  the  string  its  vibration-number  is  doubled.  At  two-thirds 
its  original  length,  it  gives  a  note  at  an  interval  of  a  fifth  above  that 
given  by  its  original  length ;  and  genera'.y  the  reciprocals  of  the  fractions 
(page  300),  representing  the  relative  vibration-numbers  of  the  several  notes 
of  a  scale,  represent  the  relative  lengths  of  the  strings  that  produce  these 
notes. 

Now,  increasing  the  weight  in  the  pail,  the  pitch  rises,  till,  when  the 
tension  is  four  pounds,  the  pitch  has  risen  an  octave.  Let  the  ten- 
sion be  the  same ;  try  another  string,  weighing,  for  the  same  length, 
four  times  as  much ;  the  pitch  is  an  octave  lower  than  that  given  by 
the  lighter  string.  (These  experiments  will  not  give  very  accurate 
results.) 

These  conclusions  may  be  summarized  by  saying :  The  vibra- 
tion-numbers of  strings  of  the  same  material  vary  inversely  as 
their  lengths  and  square  roots  of  their  weights,  and  directly  as  the 
square  roots  of  their  tension. 

QUESTIONS   AND    PROBLEMS. 

1.  Why  does    a  violinist  finger  the   strings  of    the  violin   when 
playing? 

2.  Examine  the  strings  of  a  piano,  and  ascertain  the  different  meth- 
ods by  which  a  wide  range  of  pitch  is  effected. 

3.  How  does  the  length  of  the  string  that  gives  the  note  F  compare 
with  the  length  of  the  C-striug  below  it,  other  things  being  equal? 


XLV.    OVERTONES   AND   HARMONICS. 

§  283.  Vibration  in  parts.  —  Experiment  1.  Hang  up  a  rubber 
tube  AC  (Fig.  219),  3m  long,  filled  with  sand,  fastening  both  ends. 
Pluck  it  near  the  middle,  and  it  will  swing  to  and  fro  as  a  whole  (2),  at 
a  rate  dependent  on  its  length,  tension,  etc.  Hold  it  fast  at  B  (3),  and 
pluck  it  at  a  point  half-way  between  A  and  B.  Both  halves  are  thrown 
into  independent  vibrations,  and  continue  so  to  vibrate  for  a  brief  time 
after  the  hand  is  withdrawn  from  B.  Again  hold  it  fast  at  B,  one- 
third  its  length  above  A  (4),  and  pluck  it  half-way  between  A  and  B ; 
the  length  BC  instantly  divides  itself  at  B'  into  two  equal  parts,  and 
on  withdrawing  the  hand  from  B,  the  whole  tube  is  seen  to  vibrate 
in  three  distinct  and  equal  sections.  In  a  similar  manner  it  may  be 
made  to  vibrate  in  four,  five,  etc.,  sections. 


COMPLEX  VIBRATIONS.  305 

All  of  the  above  experiments  may  be  repeated  with  the  same 
results  on  the  string  of  the  sonometer.  By  placing  paper  riders l 
along  the  string,  the  ventral  segments  and  the  nodes  can  be 
easily  discovered,  as  those  placed  near  the  center  of  the  seg- 
ments will  be  thrown  off,  Fig.  219. 
Avhile  those  at  the  nodes  will 
remain  comparatively  at  rest. 

The  sounds  coming  from 
a  string  or  other  body  that 
vibrates  in  parts  are  called 
overtones.  If,  as  is  the  case 
with  a  string  or  a  column  of 
air  in  an  organ  pipe  (page 
321),  the  vibration-number 
of  the  overtone  is  just  two, 
three,  four,  etc.,  times  that 
of  the  fundamental  or  lowest 
tone,  the  sound  is  called  a 
harmonic.  Many  overtones 
can  be  produced  from  a  steel 
bar  or  a  metallic  plate,  but 
no  harmonics.  This  distinc- 
tion is  of  great  importance, 
for,  practically,  no  musical  instruments  are  of  much  use  unless 
their  vibrating  parts  furnish  harmonics. 

§  284.  Complex  vibrations.  —  Experiment  1.  Strike  one  of 
the  lowest  notes  of  a  piano,  hold  the  key  down,  and  immediately 
apply  the  tip  of  the  finger  to  some  point  of  the  wire  struck,  and  notice 
any  changes  in  tone  that  may  occur  after  applying  the  finger.  Kepeat 
this  at  many  points  along  the  string.  If,  after  touching  the  string,  the 
fundamental  tone  continues,  it  shows  that  you  have  touched  a  node, 
and  consequently  have  not  stopped  the  vibrations  by  which  this  tone 
is  produced ;  still  you  will  notice  that  the  sound,  though  not  changed 
in  pitch,  is  changed  somewhat  in  quality  (see  page  309).  If  the  funda- 

1  Made  by  folding  narrow  strips  of  paper  in  the  middle,  eo  that  they  may  be  hung  on 
the  string. 


306  SOUND. 

mental  sound  disappears,  there  will  most  probably  be  a  sound  of  a 
higher  pitch  that  will  continue,  showing  that  although  you  have  stopped 
one  set  of  vibrations,  there  were  still  other  vibrations  in  the  string  of 
a  higher  vibration-period  which  you  did  not  stop,  and  which  now  be- 
come audible  since  the  louder  fundamental  is  silenced. 

Experiment  2.  Press  down  the  C'-key  (middle  C)  gently,  so  that 
it  will  not  sound;  and  while  holding  it  down,  strike  the  C-wire 
strongly.  In  a  few  seconds  release  the  key,  so  that  its  damper  will  stop 
the  vibrations  of  the  string  that  was  struck,  and  you  will  hear  a  sound 
which  you  will  recognize  by  its  pitch  as  coming  from  the  C'-wire. 
Place  your  finger  lightly  on  the  C'-wire,  and  you  will  find  that  it  is 
indeed  vibrating.  Press  down  the  right  pedal  with  the  foot,  so  as 
to  lift  the  dampers  from  all  the  wires,  strike  the  C-key,  and  touch 
with  the  finger  the  C'-wire ;  it  vibrates.  Touch  the  keys  next  to  C', 
viz.,  B  and  D';  they  have  only  a  slight  forced  vibration.  Touch  G'; 
it  vibrates. 

Now  it  is  evident  that  the  vibrations  of  the  Cf  and  Gr-wires 
are  sympathetic.  But  a  C-wire  vibrating  as  a  whole  cannot 
cause  sympathetic  vibrations  in  a  C'-wire ;  but,  if  it  vibrates  in 
halves,  it  may.  Hence,  we  conclude  that  when  the  C-wire  was 
struck  it  vibrated,  not  only  as  a  whole,  giving  a  sound  of  its 
own  pitch,  but  also  in  halves  ;  and  the  result  of  this  latter  set 
of  vibrations  was,  that  an  additional  sound  was  produced  by 
this  wire,  just  an  octave  higher  than  the  first-mentioned  sound. 

Again,  the  G'-wire  makes  396  vibrations  in  a  second,  or 
three  times  as  many  (132)  as  are  made  by  the  C-wire ;  hence 
the  latter  wire,  in  addition  to  its  vibrations  as  a  whole  and  in 
halves,  must  have  vibrated  in  thirds,  inasmuch  as  it  caused  the 
G'-wire  to  vibrate.  It  thus  appears  that  a  string  may  vibrate 
at  the  same  time  as  a  whole,  in  halves,  thirds,  etc.,  and  the 
result  is  that  a  sensation  is  produced  that  is  compounded  of  the 
sensations  of  several  sounds  of  different  pitch. 

Not  only  do  stringed  instruments  produce  compound  tones, 
but  no  ordinary  musical  instrument  is  capable  of  producing  a 
simple  tone,  i.e.,  a  sound  generated  by  vibrations  of  a  single 
period.  In  other  words,  when  any  note  of  any  musical  instru- 
ment is  sounded,  there  is  produced,  in  addition  to  the  primary 


CAUSE   OF   HARMONY   AND   DISCORD.  307 

tone,  a  number  of  other  tones  in  a  progressive  series,  each  tone  of 
the  series  being  usually  of  less  intensity  than  the  $>receding.  The 
primary  or  lowest  tone  of  a  note  is  usually  sufficiently  intense 
to  be  the  most  prominent,  and  hence  is  called  the  fundamental 
tone. 

§  285.  Cause  of  harmony  and  discord.  —  The  harmonics 
in  any  note  are  produced  successively  by  two,  three,  etc.,  times 
the  number  of  vibrations  made  by  its  fundamental.  Hence, 
if  any  two  notes  an  octave  apart,  —  for  instance,  C  and  C',  — 
are  sounded  simultaneously,  there  will  result  for 

C,    1,  2,  3,  4,  5,  6,  etc.,  )  ,. 

'  '  >  times  the  number  of  vibrations  made 

C',        2,       4,       6,  etc.,  j 

by  the  fundamental  of  C.  So  that  the  fundamental  of  C',  and 
each  of  its  overtones  (with  the  exception  of  the  highest,  which 
are  too  feeble  to  affect  the  general  result)  coincides  with  one  of 
the  overtones  of  C.  Not  only  is  there  perfect  agreement  among 
the  overtones  of  two  notes  an  octave  apart  when  sounded  to- 
gether, as  when  male  and  female  voices  unite  in  singing  the 
same  part  of  a  melody,  but  the  richness  and  vivacity  of  the 
sound  is  much  increased  thereby.  That  two  notes  sounded  to- 
gether may  harmonize,  it  is  essential  not  only  that  the  pitch  of 
their  fundamental  tones  be  so  widely  different  that  they  cannot 
produce  audible  beats,  but  that  no  beats  shall  be  formed  by  their 
overtones,  or  by  an  overtone  and  a  fundamental. 

For  example,  the  vibration-numbers  of  the  fundamentals  of  C;  and 
its  octave  C"  are  respectively  264  and  528,  and  the  number  of  beats  that 
they  give  is  264  in  a  second.  If,  instead  of  C",  a  note,  the  vibration- 
number  of  whose  fundamental  is  527,  is  sounded  with  C,  the  number  of 
beats  produced  by  their  fundamentals  would  be  263,  and  no  discord 
would  result  therefrom  (why?);  but  there  would  be  one  beat  per  second 
between  the  first  overtone  of  C'  and  the  fundamental  of  C",  and  this 
would  introduce  a  discord. 

Observe  that  the  relation  between  the  vibration-numbers  of 
the  fundamentals  of  C  and  C',  C  and  G,  C  and  F,  and  C,  of 
any  diatonic  scale  and  any  note  in  the  same  scale,  can  be 


308  SOUND. 

expressed  in  terms  of  small  numbers,  e.g.,  1  :  2,  2  :  3,  3  : 4,  etc. 
(see  p.  300) .  General!}',  those  notes  and  only  those  harmonize 
ivhose  fundamental  tones  bear  to  one  another  ratios  expressed 
by  small  numbers;  and  the  smaller  the  numbers  which  express 
the  ratios  of  the  rates  of  vibration,  the  more  perfect  is  the  har- 
mony of  two  sounds. 

It  follows,  from  what  has  been  said,  that  only  a  limited  num- 
ber of  notes  can  be  sounded  with  any  given  note  assumed  as  a 
prime  without  generating  discord.  Hence,  the  musical  scale  is 
limited  to  certain  determinate  degrees,  represented  by  the  eight 
notes  of  the  so-called  musical  or  diatonic  scale.  This  scale  is 
not  the  result  of  any  arbitrary  or  fanciful  arrangement,  but  is 
determined  by  the  possibility  of  its  notes  harmonizing  with  the 
prime  of  the  scale,  both  as  regards  their  fundamental  tones  and 
their  overtones. 

EXERCISES. 

1.  Prepare  a  table  of  the  series  of  overtones  of  C  and  G  respectively, 
as  on  page  307,  and  ascertain  what  overtones  of  the  two  series  har- 
momz3. 

2.  Arrange  the  notes  of  the  diatonic  scale  in  a  single  octave  in  the 
order  of  their  rank  with  reference  to  their  harmonizing  with  the  prime 
of  the  scale,  on  the  principle  that  "  the  smaller  the  numbers  which 
express  the  ratio,"  etc. 

3.  Verify  your  conclusions  as  follows :  Strike  the  C-key  of  a  piano, 
together  with  each  of  the  seven  white  keys  above  it,  consecutively,  and 
compare  the  results  of  the  different  pairs  with  reference  to  harmony. 


ANALYSIS   OF   SOUNDS.  309 

XLVI.    QUALITY   OF   SOUND. 

Let  the  same  note  be  sounded  with  the  same  intensity,  suc- 
cessively, on  a  variety  of  musical  instruments,  e.g.,  a  violin, 
cornet,  clarinet,  accordion,  jews-harp,  etc.  ;  each  instrument 
will  send  to  your  ear  the  same  number  of  waves,  and  the  waves 
from  each  will  strike  the  ear  with  the  same  force,  yet  the  ear  is 
able  to  distinguish  a  decided  difference  between  the  sounds,  — 
a  difference  that  enables  us  instantly  to  identify  the  instruments 
from  which  they  come.  Sounds  from  instruments  of  the  same 
kind,  but  by  different  makers,  usually  exhibit  decided  differences 
of  character.  For  instance,  of  two  pianos,  the  sound  of  one 
will  be  described  as  richer  and  fuller,  or  more  ringing,  or  more 
"wiry,"  etc.,  than  the  other.  No  two  human  voices  sound 
exactly  alike.  That  difference  in  the  character  of  sounds,  not 
due  to  pitch  or  intensity,  that  enables  us  to  distinguish  one 
from  another,  is  called  quality.  Two  sounds  may  differ  from 
one  another  in  loudness,  pitch,  or  quality ;  they  can  differ  in  no 
other  respect. 

Pitch  depends  on  frequency  of  vibrations,  loudness  on  their 
amplitude;  on  what  does  quality  depend? 

§  286.  Analysis  of  sounds.  — The  unaided  ear  is  unable,  ex- 
cept to  a  very  limited  extent,  to  F.  2?0 
distinguish  the  individual  tones 
that  compose  a  note.  Helmholtz 
arranged  a  series  of  resonators 
consisting  of  hollow  spheres  of 
•brass,  each  having  two  openings  : 
one  (A,  Fig.  220)  large,  for  the 
reception  of  the  sound-waves,  and 
the  other  (B)  small  and  funnel- 
shaped,  and  adapted  for  insertion 
into  the  ear.  Each  resonator  of 
the  series  was  adapted  by  its  size 
to  resound  powerfully  to  only  a 
single  tone  of  a  definite  pitch.  When  any  musical  sound  is  produced 
in  front  of  these  resonators,  the  ear,  placed  at  the  orifice  of  any  one, 


310  SOUND. 

is  able  to  single  out  from  a  collection  that  overtone,  if  present,  to 
which  alone  this  resonator  is  capable  of  responding.  It  is  found  that, 
when  a  note  is  produced  on  a  given  instrument,  not  only  is  there  a  great 
variety  of  intensity  represented  by  the  overtones,  but  all  the  possible 
overtones  of  the  series  are  by  no  means  present.  Which  are  wanting 
depends  very  much,  in  stringed  instruments,  upon  the  point  of  the 
string  struck.  For  example,  if  a  string  is  struck  in  its  middle,  no  node 
can  be  formed  at  that  point ;  consequently,  the  two  important  overtones 
produced  by  2  and  4  times  the  number  of  vibrations  of  the  fundamental 
will  be  wanting.  Strings  of  pianos,  violins,  etc.,  are  generally  struck 
near  one  of  their  ends,  and  thus  they  are  deprived  of  only  some  of  their 
higher  and  feebler  overtones. 

§  287.  Synthesis  of  sounds.  —  The  sound  of  a  tuning-fork, 
when  its  fundamental  is  reenforced  by  a  suitable  resonance-cavity,  is 
very  nearly  a  simple  tone.  By  sounding  simultaneously  several  forks 
of  different  but  appropriate  pitch,  and  with  the  requisite  relative  inten- 
sities, Helmholtz  succeeded  in  reproducing  sounds  peculiar  to  various 
musical  instruments,  and  even  in  imitating  most  of  the  vowel  sounds 
of  the  human  voice. 

Thus  it  appears  that  he  has  been  able  to  determine,  both 
analytically  and  synthetically,  that  the  quality  of  a  given  sound 
depends  upon  what  overtones  combine  with  its  fundamental,  and 
on  their  relative  intensities;  or,  we  may  say  more  briefly,  upon 
the  form  of  vibration,  since  the  form  must  be  determined  by 
the  character  of  its  components. 


METHOD   OF   REPRESENTING   SOUND   VIBRATIONS.       311 


XLVII.  COMPOSITION  OF  SONOROUS  VIBRATIONS,  AND  THE 
RESULTANT    WAVE-FORMS. 

§  288.  Method  of  representing  sound  vibrations  graph- 
ically. —  It  is  evident  that  there  must  be  a  particular  aerial 
wave-form  corresponding  to  each  compound  vibration,  other- 
wise the  ear  would  not  be  able  to  appreciate  a  difference  in 
quality  of  sounds  to  which  these  combination-forms  give  rise. 
Every  particle  of  air  engaged  in  transmitting  a  compound  sound 
is  simultaneously  acted  upon  by  several  sets  of  vibratory  move- 
ments, and  it  remains  to  investigate  what  its  motion  will  be 
under  their  joint  influence. 


Fig.  221. 


The  light  wave-lines  AB  (Fig.  221)  represent  typically  two 
series  of  aerial  sound-waves,  corresponding  respectively  to  a 
fundamental  and  its  first  overtone.  Thejieavy  line  represents 
the  form  of  the  joint  wave  which  results  from  the  combination 
of  the  two  constituents.  If  we  suppose  lines  perpendicular  to  the 
axis,  that  is,  to  the  dotted  line,  or  line  of  repose,  to  be  drawn 
to  each  point  in  this  line,  as  a&,  cd,  eF,  etc.,  they  will  represent 
by  their  varying  lengths  the  displacement  of  any  particle  in  a 
vibrating  body,  or  any  particle  of  air  traversed  by  sound-waves, 
from  its  normal  position. 

The  rectangular  diagram  C  D  is  intended  to  represent  a  por- 
tion of  a  tranverse  section  of  a  body  of  air  traversed  by  the 
joint  wave  represented  by  the  heavy  wave-line  above.  The 


312 


SOUND. 


depth  of  shading  in  different  parts  indicates  the  degree  of  con- 
densation at  those  parts. 

Figure  222  represents  wave-lines  drawn  by  an  instrument  called  a 
vibrograph.  The  second  line  represents  a  sound  two  octaves  above 
that  which  the  first  line  represents,  and  the  third  line  shows  the  result 
of  the  combination  of  the  two  sets  of  vibrations. 

Fig.  222. 


Fig.  223. 


In  an  elaborate  apparatus  called  the  logograph,  a  thin  membrane  of 
gold-beater's  skin  carries  a  marker  resembling  the  point  of  a  stylo- 
graphic  pen.  When  a  person  sings  or  talks  to  this  membrane,  it  traces 
upon  paper  a  graphic  representation  of  the  varying  air  pressure.  That 
is,  all  the  changes  in  the  density  of  the  air,  and  all  the  movements  of  a 
given  air-particle  during  the  passage  of  the  sound-waves,  are  faithfully 
aepicted  in  a  line  traced  by  the  marker  on  a  passing  paper ;  just  as  the 
iieavy  wave-line  AB  (Fig.  221)  may  be  said  to  represent  the  condition 
of  the  air  CL>,  or  of  the  motion  of  any  particle  of  it,  supposing  that 
a  marker  were  attached  to  it  and  a  paper  drawn  beneath  it  at  right 
angles  to  die  path  of  its  motion.  The  diagram  in  Figure  223  shows  the 
result  produced  oy  pronouncing  the  sentence  there  given  at  the  rate 
of  six  syllables  in  a  second. 

§  289.  Manometric  flames.  —  Apparatus  like  that  shown 
in  Figure  224  may  be  very  easily  prepared,  and  will  serve  to  illustrate  in 
a  pleasing  manner  many  facts  pertaining  to  sound.  Procure  a  wooden 
pill-box  or  tooth-pick  box  A,  having  a  capacity  of  50  to  100ccm.  Across 
the  top  of  the  open  box  stretch  tightly  a  circular  piece  of  gold-beater's 


MANOMETRTC   FLAMES. 


313 


skin  a,  and  glue  it  at  its  edges  so  that  it  may  cover  the  box  like  the 
head  of  a  drum.  Crowd  on  the  cover,  and  the  box  will  have  two  com- 
partments, b  and  c.  Through  the  bottom  of  the  box,  and  through  the 
cover,  pass  glass  tubes  e  and  d,  opening  into  the  compartments.  Also 
introduce  another  tube  n  through  the  side  of  the  cover.  Connect  the 
last  tube  by  means  of  a  rubber  tube  with  a  gas  burner.  Attach  a  piece 
of  large-sized  rubber  tube  to  the  glass  tube  e,  and  into  the  other  ex- 
tremity of  the  rubber  tube  introduce  the  small  end  of  a  pasteboard 
cone  B.  The  tube  d  Fi?.  224. 

should  be  drawn  out 
so  as  to  be  able  to 
give  a  small  flame. 
Place  two  thin  glass 
mirrors  M,  abo.it 
14cm  square,  back  to 
back,  and  secure 
them  by  light  frames 
at  the  top  and  bot- 
tom, and  in  the  cen- 
ter of  each  frame 
insert  small  rods  C 
and  D. 

Light  the  gas1  at 
the  extremity  of  d, 
and  hold  the  mirror 
vertically,  and  at  a 
short  distance  from 
the  flame  F ;  an  im- 
age of  the  flame  will 
appear  in  the  mirror, 
as  represented  by  A 
(Fig.  225).  Eotate 
the  mirror,  and  the 
(lame  appears  drawn  out  in  a  band  of  light,  as  shown  in  B  of  the  same 
figure. 

Now  sing  into  the  cone  B  (Fig.  224),  the  sound  of  oo  in  tool,  and 
waves  of  air  will  run  down  the  tube,  beat  against  the  membrane  a,  as 
against  the  drum-head  of  the  ear  (see  §  290),  causing  it  to  vibrate,  and 
the  membrane  in  turn  acts  upon  the  gas  in  the  compartment  c,  throwing 
it  into  vibration.  The  result  is,  that  instead  of  a  flame  appearing  in  the 
rotating  mirror  as  a  continuous  band  of  light,  it  is  divided  up  into  a 

>  If  gas  is  not  accessible,  the  end  of  the  tube  d  may  be  inserted  In  a  candle  flame,  and 
good  results  obtained. 


314: 


SOUND. 


series  of  tongues  of  light,  as  shown  in  C  of  Figure  225,  each  condensa- 
tion being  represented  by  a  tongue,  and  each  rarefaction  by  a  dark 
interval  between  the  tongues.  If  a  note  an  octave  higher  than  the  last 
is  sung,  we  obtain,  as  we  should  expect,  twice  as  many  toiigues  in  the 

Fig.  225. 


same  space,  as  shown  in  D.  E  represents  the  result  when  the  two 
tones  are  produced  simultaneously,  and  illustrates  in  a  striking  manner 
the  effect  of  interference.  (Explain.)  F  represents  the  result  when 
the  vowel  e  is  sung  on  the  key  of  C' ;  and  G,  when  the  vowel  o  is  sung 
on  the  same  key.  These  are  called  manometric  flames. 


THE  EAR. 


315' 


XLVIII.    SOME   SOUND-RECEIVING  INSTRUMENTS. 

§  290.  The  ear. —In  Figure  226,  A  represents  the  external  ear- 
passage;  a  is  a  membrane,  called  the  tympanum,  a  little  thicker  than 
gold-beater's  skin,  stretched  across  the  bottom  of  the  passage,  and 
thus  closing  the  orifice  of  a  cavity  b  in  the  bones  of  the  skull  called  the 
drum;  c  is  a  chain  of  small  bones  stretching  across  the  drum,  and  con- 
necting the  tympanum  with  the  thin  membranous  wall  of  the  vestibule 
e ;  ff  are  a  series  of  semicircular  canals  opening  into  the  vestibule; 

Fig.  226. 


g  is  the  opening  iuto  another  canal  in  the  form  of  a  snail-shell  g!, 
hence  called  the  cochlea  (this  is  drawn  on  a  reduced  scale)  ;  d  is  a  tube 
(the  Eustachian  tube}  connecting  the  drum  with  the  throat ;  and  h  is 
the  auditory  nerve.  The  vestibule  and  all  the  canals  opening  into  it 
are  filled  with  a  transparent  liquid  which  is  mainly  water.  The  drum 
of  the  ear  contains  air,  and  the  Eustachian  tube  forms  a  means  of 
ingress  and  egress  of  air  through  the  throat. 

Now  how  does  the  ear  hear  ?  and  how  is  it  able  to  distinguish 
between  the  infinite  variety  of  form,  rapidity,  and  intensity  of 


316  SOUND. 

aerial  sound-waves,  so  as  to  interpret  correctly  the  correspond- 
ing qualit}7,  pitch,  and  loudness  of  sound  ?  Sound-waves  enter 
the  external  ear-passage  A  as  ocean- waves  enter  the  bays  of  the 
sea-coast,  are  reflected  inward,  and  strike  the  tympanum.  The 
air-particles,  beating  against  this  drum-head,  impress  upon  it 
the  precise  wave-form  that  is  transmitted  to  it  through  the  air 
from  the  sounding  body.  The  motion  received  by  the  drum- 
head is  transmitted  by  the  chain  of  bones  to  the  membranous 
wall  of  the  vestibule.  From  the  walls  of  this  cavity  project 
into  its  liquid  contents  thousands  of  fine  elastic  threads  or 
fibres,  which  we  may,  for  convenience,  call  bristles.  Especially 
in  the  spiral  passage  of  the  cochlea,  as  it  becomes  smaller  and 
smaller,  these  vibratile  bristles  become  of  gradually  diminishing 
length  and  size  (such  as  the  wires  of  a  piano  may  roughly 
represent) ,  and  are  therefore  suited  to  respond  sympathetically 
to  a  great  variety  of  vibration-periods.  This  arrangement  is 
sometimes  likened  to  a  harp  of  three  thousand  (this  being 
about  the  number  of  bristles)  strings.  The  auditory  nerve  at 
its  extremity  is  divided  into  a  large  number  of  filaments,  like 
a  cord  unravelled  at  its  end,  and  one  of  these  filaments  is 
attached  to  each  bristle.  Now,  as  the  sound-waves  reach 
the  membranous  wall  of  the  vestibule,  they  set  it,  and  by 
means  of  it  the  liquid  contents,  into  forced  vibration,  and  so 
through  the  liquid  all  the  fibres  receive  an  impulse.  Those 
bristles  whose  vibration-periods  correspond  with  the  periods  of 
the  constituents  forming  the  compound  wave  are  thrown  into 
sympathetic  vibration.  The  bristles  stir  the  nerve  filaments, 
and  the  nerve  transmits  to  the  brain  the  impressions  received. 
Just  as  a  piano,  when  its  dampers  are  raised  and  a  person  sings 
into  it,  may  be  said  to  anatyze  each  sound,  and  show  by  the 
vibrating  strings  of  how  many  tones  it  is  composed,  as  well  as 
their  respective  pitch,  and  by  the  amplitude  of  their  vibrations 
their  respective  intensities  ;  so  it  is  thought  this  wonderful  harp  of 
the  ear  analyzes  every  complex  sound-wave  into  a  series  of  simple 
vibrations.  Tidings  of  the  disturbances  are  communicated  to  the 


THE   PHONOGRAPH. 


317 


Fig.  227. 


brain,  and  there,  in  some  mysterious  manner,  these  disturbances 
are  interpreted  as  sound  of  definite  quality,  pitch,  and  intensity. 

§  291.  Phonograph.  —  Figure  227  represents  a  vertical  sec. 
tion  of  the  Edison  phonograph.  A  metallic  cylinder  A  is  rotated  by 
means  of  a  crank  B  in  the  direction  indicated  by  the  arrow.  On  the  sur- 
face of  the  cylinder  is  cut  a  shallow 
spiral  groove  running  around  the 
cylinder  from  end  to  end,  like  the 
thread  of  a  screw.  A  small  metallic 
point,  or  style,  projecting  from  the  B 
under  side  of  a  thin  metallic  disk  o, 
which  closes  one  orifice  of  the  mouth- 
piece C,  stands  directly  over  the 
thread.  By  a  simple  device  the  cyl- 
inder, when  the  crank  is  turned,  is 
made  to  advance  just  rapidly  enough 
to  allow  the  groove  to  keep  constantly 
under  the  style.  The  cylinder  is  cov- 


Fig.  228. 


ered  with  tinfoil.     The  space  E  represents  the  space  (greatly  exag- 
gerated) between  the  tinfoil  and  the  bottom  of  the  groove. 

Now,  when  a  person  directs  his  voice  toward  the  mouth-piece,  the 
aerial  waves  cause  the  disk  o  to  participate  in  every  mo'tion  made  by 
the  particles  of  air  as  they  beat  against  it,  and  the  motion  of  the  disk 
is  communicated  by  the  style  to  the  tinfoil,  pro- 
ducing thereon  impressions  or  indentations  as  it 
passes  on  the  rotating  cylinder.  The  result  is  that 
there  is  left  upon  the  foil  an  exact  representation 
in  relief  of  every  movement  made  by  the  style.  Some  of  the  indenta- 
tions are  quite  perceptible  to  the  naked  eye,  while  others  are  visible 
only  with  the  aid  of  a  microscope  of  high  power.  Figure  228  repre- 
sents a  piece  of  the  foil  as  it  would  appear  inverted  after  the  indenta- 
tions (here  greatly  exaggerated)  have  been  imprinted  upon  it. 

The  words  addressed  to  the  phonograph  having  been  thus  impressed 
upon  the  foil,  the  mouth-piece  and  style  are  temporarily  removed,  while 
the  cylinder  is  brought  back  to  the  position  it  had  when  the  talking 
began,  and  then  the  mouth-piece  is  replaced.  Now,  evidently,  if  the 
crank  is  turned  in  the  same  direction  as  before,  the  style,  resting  upon 
the  foil  beneath,  will  be  made  to  play  up  and  down  as  it  passes  over 
ridges  and  sinks  into  depressions ;  this  will  cause  the  disk  o  to  repro- 
duce the  same  vibratory  movements  that  caused  the  ridges  and  depres- 


318  SOUND. 

sions  in  the  foil.  The  vibrations  of  the  disk  are  communicated  to  the 
air,  and  through  the  air  to  the  ear ;  and  thus  the  words  spoken  to  the 
apparatus  may  be,  as  it  were,  shaken  out  into  the  air  again  at  any 
subsequent  time,  even  centuries  after,  accompanied  by  the  exact 
accents,  intonations,  and  quality  of  sound  of  the  original. 

§  292.  String  telephone.  — In  the  phonograph,  the  metallic  disk 
serves,  as  it  were,  alternately,  as  an  ear  and  a  tongue.  If,  instead  of 
the  same  disk  being  made  to  do  double  duty,  two  disks  (or,  better,  two 
membranes  of  gold-beater's  skin  or  bladder)  connected  by  a  thread  are 
used,  either  one  of  which  may  serve  as  a  tongue  and  the  other  simul- 
taneously as  an  ear,  conversation  may  be  carried  on  by  means  of  them 

A  Fig  229  B     throuSh  considerable  distances. 

^^  _^^  Figure  229  represents  such  an 

^S  arrangement,  which  constitutes 

the  well-known,  instructive  toy,  called  the  lover's  telegraph,  though  it 
is  more  properly  a  telephone. 

The  thread  is  attached  at  each  extremity  to  the  centers  of  the  mem- 
branes which  cover  one  orifice  of  each  of  the  tin  speaking-tubes  A  and 
B,  by  passing  the  thread  through  the  membranes,  and  tying  the  knots 
at  the  ends.  A  person  speaking  into  one  of  the  tubes  throws  its 
membrane  into  vibration ;  these  impulses  are  communicated  through 
the  string  to  the  other  membrane,  which  is  thus  caused  to  vibrate  in 
unison  with  the  first.  If  now  another  person  place  his  ear  near  the 
latter  membrane,  he  can  hear  distinctly  the  words  spoken  by  the  first 
person,  though  a  quarter  of  a  mile  distant,  while  other  persons  sta- 
tioned midway  between  these  two  hear  nothing. 

It  seems  fair  to  presume,  that  if  the  movements  of  the  hand  or 
of  machinery  could  be  rendered  sufficiently  delicate  to  imitate  these 
minute  movements  of  the  membrane,  talking  might  be  accomplished 
with  the  hand  or  machinery ;  for  talking,  after  all,  is  only  mechanical 
motion. 

§  293.  Electric  telephone. — In  this  telephone  the  vibrations 
of  one  disk  are  reproduced  in  another  through  the  agency  of  electricity, 
as  explained  on  page  270. 


SOUNDING   AIR-COLUMNS.  319 


XLIX.    MUSICAL  INSTRUMENTS. 

§  294.  Musical  instruments  may  be  grouped  in  three  classes  : 
(1)  Stringed  instruments ;  (2)  wind  instruments,  in  which  the 
sound  is  due  to  the  vibration  of  columns  of  air  confined  in  tubes  ; 
(3)  instruments  in  which  the  vibrator  is  a  membrane  or  plate. 
The  first  class  has  received  its  share  of  attention  ;  the  other  two 
merit  a  little  further  consideration. 

§295.  Sounding  air-columns.  — Experiment  1.  Take  four 
glass  tubes,  A,  B,  C,  and  D,  respectively  48,  48,  24,  and  12cm  long,  and 
about  2.5cm  diameter.  Blow  gently  across  one  of  the  ends  of  each ;  C 
gives  a  sound  an  octave  higher  than  A  or  B,  and  D  an  octave  higher 
than  C.  Close  one  of  the  ends  of  B,  C,  and  D,  and  repeat  the  experi- 
ment, and  you  will  find  that  the  notes  obtained  from  these  three  have 
still  the  same  relation  to  one  another.  Blow  across  one  end  of  A, 
which  is  open  at  both  ends,  and  across  the  open  end  of  B ;  A  gives 
a  note  about  an  octave  higher  than  B. 

These  experiments  show  (1)  that  the  pitch  of  vibrating  air- 
columns,  as  well  as  of  strings,  varies  with  the  length,  and  in  both 
stopped1  and  open  pipes  the  number  of  vibrations  is  inversely  pro- 
portional to  the  length  of  the  pipe2;  (2)  that  an  open  pipe  gives 
a  note  an  octave  higher  than  a  dosed  pipe  of  the  same  length. 

Experiment  2.  —  Blow  across  the  orifice  of  B  as  before,  gradually 
increasing  the  force  of  the  current.  It  will  be  found  that  only  the 
gentle  current  will  give  the  full  musical  fundamental  tone  of  the  tube,  — 
a  little  stronger  current  produces  a  mere  rustling  sound ;  but  when  the 
force  of  the  current  reaches  a  certain  limit,  an  overtone  will  break 
forth ;  and,  on  increasing  still  further  the  power  of  the  current,  a  still 
higher  overtone  may  be  reached. 

Figure  230  represents  an  open  organ-pipe  provided  with  a  glass 
window  A  in  one  of  its  sides.  A  wire  hoop  B  has,  stretched  over  it,  a 
membrane,  and  the  whole  is  suspended  by  a  thread  within  the  pipe.  If 
the  membrane  is  placed  near  the  upper  end,  a  buzzing  sound  proceeds 

1  A  stopped  pipe  is  one  which  is  closed  at  one  end. 

2  The  diameter  has  the  same  influence  here  as  in  the  resonance-jar  (p.  293),  but  we 
shall  neglect  it. 


320 


SOUND. 


Fig.  230. 


Fig.  231. 


from  the  membrane  when  the  fundamental  of  the  pipe  is  sounded ;  and 
sand  placed  on  the  membrane  will  dance  up  and  down  in  a  lively  man- 
ner.  On  lowering  the  membrane,  the  buzzing  sound  becomes  fainter, 
till,  at  the  middle  of  the  tube,  it  ceases  entirely,  and  the 
sand  becomes  quiet.  Lowering  the  membrane  still  further, 
the  sound  and  dancing  recommence,  and  increase  as  the 
lower  end  is  approached. 

It  is  thus  found,  that  (3)  when  the  fundamental  of 
an  open  pipe  is  sounded,  its  air-column  divides  itself 
into  two  equal  vibrating  sections,  with  the  antinodes 
at  the  extremities  of  the  tube,  and  a  node  in  the 
center. 

If  the  pipe  is  stopped,  there  is  a  node  at  the 
stopped  end  ;  if  it  is  open,  there  is  an  antinode  at  the 
open  end ;  and  in  both  cases  there  is  an  antinode  at 
the  end  where  the  wind  enters,  which  is  always  to  a 
certain  extent  open. 

A,  B,  and 
C  of  Figure 
231  show 
respectively 
the  positions 
of  the  nodes 
and  anti- 
nodes  for  the  fundamen- 
tal and  first  and  second 
overtones  of  a  closed 
pipe ;  and  Ar,  B',  and  C' 
show  the  positions  of 
the  same  in  an  open  pipe 
of  the  same  length.  The 
distance  between  the 
dotted  lines  shows  the 
relative  amplitudes  of 
the  vibrations  of  the 
air-particles  at  various 
points  along  the  tube. 

Now  the  distance  between  a  node  and  its  nearest  antinode  is  a  quarter 
of  a  wave-length.     Comparing  then  A  and  A',  it  will  be  seen  that  the 


SOUNDING  PLATES. 


321 


wave-length  of  the  fundamental  of  the  closed  pipe  must  be  twice  the 
wave-length  of  the  fundamental  of  the  open  pipe ;  hence  the  vibration- 
period  of  the  latter  is  half  that  of  the  former ;  consequently  the  funda- 
mental of  the  open  pipe  must  be  an  octave  higher  than  that  of  the 
closed  pipe. 

The  number  of  segments  into  which  the  length  of  the  air-col- 
umn is  divided,  in  the  three  cases  of  the  closed  tube,  are  respec- 
tively -|,  f ,  and  f ;  hence  the  corresponding  vibration-numbers 
are  as  1:3:5,  etc.  Hence,  (4)  in  dosed  tubes,  only  those  over- 
tones whose  vibration-numbers  correspond  to  the  odd  multiples  of 
the  fundamental  are  present. 

The  number  of  segments  into  which  the  length  of  the  air-col- 
umn is  divided,  in  the  three  cases  of  the  open  tube,  are  respec- 
tivel}r  -f ,  -f ,  and  -f ;  their  vibration-numbers  are  therefore  as 
1  :  2  : 3,  etc.  Hence,  (5)  in  open  tubes,  the  complete  series  of 
overtones  corresponding  to  its  fundamental  are  present. 

Fig.  232. 


§  296.  Sounding  plates. — Experiment.  Procure  at  a  hard- 
ware store  a  perfectly  flat  piece  of  sheet  brass  2mm  thick  and  20cm 
square.  Fasten  it  at  its  center  to  a  supporting  rod  A,  Figure  232. 
Scatter  on  the  plate  some  fine  sand,  and  draw  a  resined  bow  steadily 


322  SOUND. 

and  firmly  over  one  of  its  edges  near  a  corner ;  and  at  the  same  time 
touch  the  middle  of  one  of  its  edges  with  the  tip  of  the  finger ;  a  musi- 
cal sound  will  be  produced,  and  the  sand  will  dance  up  and  down,  and 
quickly  collect  in  two  rows,  extending  across  the  plate  at  right  angles 
to  one  another.  Draw  the  bow  across  the  middle  of  an  edge,  and  touch 
with  a  finger  one  of  its  corners,  and  the  sand  will  arrange  itself  in  two 
diagonal  rows  (2)  across  the  plate,  and  the  pitch  of  the  note  will  be  a 
fifth  higher.  Touch,  with  the  nails  of  the  thumb  and  forefinger,  two 
points  a  and  b  (3)  on  one  edge,  and  draw  the  bow  across  the  middle  c 
"of  the  opposite  edge,  and  you  will  obtain  additional  rows  and  a  shriller 
note. 

By  varying  the  position  of  the  points  touched  and  bowed,  a 
great  variety  of  patterns  can  be  obtained,  some  of  them  exceed- 
ingly complicated  and  beautiful.  It  will  be  seen  that  the  effect 
of  touching  the  plate  with  a  finger  is  to  prevent  vibration  at  that 
point,  and  consequently  a  node  is  there  produced.  The  whole 
plate  then  divides  itself  up  into  segments  with  nodal  division 
lines  in  conformity  with  the  node  just  formed.  The  sand  rolls 
away  from  those  parts  which  are  alternately  thrown  into  crests 
and  troughs,  to  the  parts  that  are  at  rest. 

§  297.  Interference.  —  Experiment.  Provide  a  tin  tube  C, 
Figure  232,  lm  long  and  5cm  in  diameter,  made  in  two  parts  so  as  to 
telescope  one  within  the  other.  The  extremity  of  one  of  the  parts 
terminates  in  two  slightly  smaller  branches.  Bow  the  plate,  as  in  the 
first  experiment  (1),  place  the  two  orifices  of  the  branches  over  the 
segments  marked  with  the  +  signs,  and  regulate  the  length  of  the  tube 
so  as  to  reenforce  the  note  given  by  the  plate,  and  set  the  plate  in 
vibration.  Now  turn  the  tube  around,  so  that  one  orifice  may  be  over 
a  +  segment,  and  the  other  over  a  —segment;  the  sound  due  to  reso- 
nance entirely  ceases.  It  thus  appears  that  the  two  segments  marked 
4-  pass  through  the  same  phases  together;  likewise  the  phases  of 
—segments  correspond  with  one  another;  i.e.,  when  one  -fsegment  is 
bent  upward,  the  other  is  bent  upward,  and  at  the  same  time  the  two 
—segments  are  bent  downward  ;  for,  when  the  two  orifices  of  the  tube 
are  placed  over  two  -{-segments  or  two  —segments,  two  condensa- 
tions followed  by  two  rarefactions  pass  up  these  branches  and  unite 
at  their  junction  to  produce  a  loud  sound ;  but  when  one  of  the  orifices 
is  over  a  +segment  and  the  other  over  a  —segment,  a  condensation 


VOCAL   ORGANS.  323 

passes  up  one  branch  at  the  same  time  that  a  rarefaction  passes  up  the 
other,  and  the  two  destroy  one  another  when  they  come  together;  i.e., 
the  two  sound-waves  combine  to  produce  silence. 

§  298.  Bells.  —  A  bell  or  goblet  is  subject  to  the  same  laws 
of  vibration  as  a  plate. 

Experiment.  —  Nearly  fill  a  goblet  with  water,  strew  upon  the  sur- 
face lycopodium  powder,  and  draw  a  resined  bow  gently  across  the  edge 
of  the  glass.  The  surface  of  the  water  will  become  rippled  with  wave- 
lets radiating  from  four  points  90°  apart,  corresponding  to  the  cen- 
ters of  four  ventral  segments  into  which  the  bell  is  divided,  and  the 
powder  will  collect  in  lines  proceeding  from  the  nodal  points  of  the 
bell.  By  touching  the  proper  points  of  a  bell  or  glass  with  a  finger- 
nail, it  may  be  made  to  divide  itself,  like  a  plate,  into  6,  8,  10,  etc., 
(always  an  even  number)  vibrating  parts. 

§  299.  Vocal  organs.  —  It  is  difficult  to  say  which  is  more 
to  be  admired,  —  the  wonderful  capabilities  of  the  human  voice 
or  the  extreme  simplicity  of  the  means  by  which  it  is  produced. 
The  organ  of  the  voice  is  a  reed  instrument  situated  at  the  top 
of  the  windpipe  or  trachea.  A  pair  of  Fig-  233. 

elastic  bands  a  a,  Figure  233,  called  the 
vocal  chords,  is  stretched  across  the  top 
of  the  windpipe.  The  air-passage  &, 
between  these  chords,  is  open  while  a 
person  is  breathing  ;  but  when  he  speaks 
or  sings  they  are  brought  together  so 
as  to  form  a  narrow,  slit-like  opening, 
thus  forming  a  sort  of  double  reed, 
which  is  made  to  vibrate,  when  air  is 
forced  from  the  lungs  through  the  nar- 
row passage,  somewhat  like  the  little 
tongue  of  a  toy  trumpet.  The  sounds  are  grave  or  high  accord- 
ing to  the  tension  of  the  chords,  which  is  regulated  by  muscu- 
lar action.  The  cavities  of  the  mouth  and  the  nasal  passages 
form  a  compound  resonance-tube.  This  tube  adapts  itself,  by 


324  SOUND. 

its  varying  width  and  length,  to  the  pitch  of  the  note  produced 
by  the  vocal  chords.  Place  a  finger  on  the  protuberance  of 
the  throat  called  the  Adam's  apple,  and  sing  a  low  note  ;  then 
sing  a  high  note,  and  you  will  observe  that  the  protuberance  rises 
in  the  latter  case,  thus  shortening  the  distance  between  the  vocal 
chords  and  the  lips.  Set  a  tuning-fork  in  vibration,  open  the 
mouth  as  if  about  to  sing  the  corresponding  note,  place  the 
fork  in  front  of  it,  and  the  cavity  of  the  mouth  will  resound  to 
the  note  of  the  fork,  but  will  cease  to  do  so  when  the  mouth 
adapts  itself  to  the  production  of  some  other  note.  The  differ- 
ent qualities  of  the  different  vowel  sounds  are  produced  by  the 
varying  form  of  the  resonating  mouth- cavit}7,  the  pitch  of  the 
fundamentals  given  by  the  vocal  chords  remaining  the  same. 
This  constitutes  articulation. 


CHAPTER  VI. 
RADIANT  ENERGY. -LIGHT. 

L.  INTRODUCTION. 

§  300.  Light  a  form  of  energy.  —  Exposed  to  the  sun,  the 
skin  is  warmed,  and  thus  the  sense  of  touch  is  affected ;  it  is 
illuminated,  and  thereby  the  sense  of  sight  is  affected ;  it  is 
tanned,  and  thereby  its  chemical  condition  is  changed.  It  is  evi- 
dent that  we  receive  something  which  must  come  to  us  from  the 
sun.  To  the  sense  of  touch  it  appears  to  be  heat ;  to  the  eye 
it  is  light ;  to  certain  substances  it  is  a  power  to  produce  chemi- 
cal changes.  But  what  is  it  that  we  receive  Fj{?  234 
from  the  sun? 

Experiment.  —  Blacken  one-half  of  one  side  of  a 
slip  of  glass  with  candle-smoke.  With  a  convex 
lens,  sometimes  called  a  "  burning-glass,"  converge 
the  sun's  light  upon  the  blackened  portion  so  as  to 
produce  a  small  luminous  spot  on  the  black  surface. 
This  spot  quickly  becomes  very  hot,  but  the  lens 
meantime  remains  comparatively  cold.  Move  the 
luminous  spot  to  the  unblackened  portion  of  the 
glass.  The  spot  becomes  only  slightly  heated. 
Place  a  piece  of  paper  behind  and  in  contact  with 
the  glass,  and  it  quickly  burns. 

Whether  we  receive  heat  from  the  sun  or 
not,  it  is  evident  that  we  receive  something 
that  can  be  converted  into  heat. 

Figure  234  represents  an  instrument  called 
a  radiometer.     The  moving  part  is  a  small  vane  resting  on  the 
point  of  a  needle.     It  is  so  nicely  poised  on  this  pivot  that  it 


326  RADIANT   ENERGY. — LIGHT. 

rotates  with  the  greatest  freedom.  To  the  extremities  of  each 
of  the  four  arms  of  the  vane  are  attached  disks  of  aluminum 
which  are  white  on  one  side  and  black  on  the  other.  The  whole 
is  enclosed  in  a  glass  bulb  from  which  the  air  is  exhausted  till 
less  than  y^n  of  the  original  quantity  is  left.  If  the  instrument 
is  exposed  to  the  sun's  light,  or  even  to  the  light  of  a  candle, 
the  wheel  will  rotate  with  the  unblackened  faces  in  advance. 

In  just  what  manner  it  is  caused  to  rotate  does  not  concern 
us ;  but  the  fact  that  it  does  rotate,  and  that  it  is  caused  to 
rotate  directly  or  indirect!}7  by  something  that  comes  from  the 
sun  or  the  candle,  is  pertinent  to  the  question  before  us.  When- 
ever a  body  is  caused  to  move  or  increase  its  rate  of  motion, 
energy  must  be  imparted  to  it ;  hence  energy  must  be  imparted 
to  the  radiometer- vane  by  the  sun  or  candle. 

Bell,  the  inventor  of  the  telephone,  has  succeeded  in  produc- 
ing musical  sounds  by  the  action  of  sun-light  and  other  intense 
lights.  But  sound  always  originates  in  motion,  and  motion 
springs  only  from  some  form  of  energy.  So,  then,  that  which  we 
receive  from  the  sun,  whether  it  affects  the  sense  of  touch  and  is 
catted  heat,  or  the  eye  and  is  called  light,  or  produces  chemical 
changes  and  is  called  chemism,  is  in  reality  some  form  of  energy. 

§  301.  Ether  the  medium  of  motion.  —  If  light  is  motion, 
what  moves  ?  Our  atmosphere  is  but  a  thin  investment  of  the 
earth,  while  the  great  space  that  separates  us  from  the  sun  con- 
tains no  air  or  other  known  substance.  But  empty  space  can 
neither  receive  nor  communicate  motion.  It  is  assumed  —  it  is 
necessary  to  assume  —  that  there  is  some  medium  filling  the 
interplanetary  space,  in  fact,  filling  all  otherwise  unoccupied 
space  (i.e.,  where  matter  is  not,  ether  is),  by  which  motion 
can  be  communicated  from  one  point  in  the  otherwise  empty 
space  to  another.  This  medium  has  received  the  name  of  ether. 
Ether  is  supposed  to  penetrate  even  among  the  molecules  of 
liquid  and  solid  matter,  and  thus  surrounds  every  molecule  of 
matter  in  the  universe,  as  the  atmosphere  surrounds  the  earth. 


UNDULATORY   THEORY   OF   LIGHT.  327 

No  vacuum  of  this  medium  can  be  obtained ;  an  attempt  to 
pump  it  out  of  a  space  would  be  like  trying  to  pump  water 
with  a  sieve  for  a  piston.  We  cannot  see,  hear,  feel,  taste, 
smell,  weigh,  nor  measure  it.  What  evidence,  then,  have  we 
that  it  exists  ?  You  believe  that  a  horse  can  see ;  you  have  no 
absolute  knowledge  of  the  fact.  But  you  reason  thus :  he  be- 
haves as  i/he  could  see  ;  in  other  words,  you  are  able  to  account 
for  his  actions  on  the  hypothesis  that  he  can  see,  and  on  no 
other.  Phenomena  occur  just  as  they  would  occur  if  all  space 
were  filled  with  an  ethereal  medium  capable  of  transmitting 
motion,  and  we  can  account  for  these  phenomena  on  no  other 
hypothesis ;  hence  our  belief  in  the  existence  of  the  medium. 

The  transmission  of  energy  through  the  medium  of  ether  is 
called  radiation  ;  energy  so  transmitted  is  called  radiaiit  energy, 
and  the  body  emitting  energy  in  this  manner  is  called  a  radiator. 
Sound  is  another  form  of  radiant  energy  transmitted  through 
solid,  liquid,  or  gaseous  media. 

§  302.  Undulatory  theory  of  light.  —  Is  motion  commu- 
nicated by  a  transfer  of  a  medium  or  by  a  transfer  of  vibrations, 
i.e.,  by  undulations  ?  All  evidence  points  to  one  conclusion: 
that  we  receive  energy  from  the  sun  in  the  form  of  vibrations  or 
wave-action ;  that  these  vibrations,  inaudible  to  our  ears,  cause 
through  the  eye  the  sensation  of  sight,  and  through  the  hand  the 
sensation  of  warmth.  This  is  known  as  the  undulatory  theory  of 
light.  To  learn  what  the  special  evidences  of  the  correctness 
of  this  theory  are,  the  pupil  must  wait  for  further  development 
of  our  subject ;  but  it  should  be  borne  in  mind  that  the  strongest 
proof  of  the  correctness  of  any  theory  is  its  exclusive  competence 
to  explain  phenomena.  Light  is  vibration  that  may  be  appre- 
ciated by  the  organ  of  sight. 

§  303.  Light  itself  invisible.  —  Darken  a  room,  and  ad- 
mit a  sunbeam  through  a  small  nail-  or  key-hole.  You  can 
trace  its  path  through  the  room  only  by  particles  of  dust  float- 
ing in  the  room.  But  if  the  air  in  a  certain  space  is  cleansed  of 


328  RADIANT    ENERGY.  —  LIGHT. 

dust,  the  path  of  a  sunbeam  through  this  space  will  be  totally 
dark.  If  the  eye  is  placed  in  its  path,  or  any  object  upon  which 
it  may  strike,  you  become  aware  of  its  presence,  not  by  seeing 
the  light,  but  by  seeing  the  object  which  sends  you  the  light. 

§  304.  Light  travels  in  straight  lines.  —  The  path  of  the 
light  admitted  into  a  darkened  room  through  a  small  aperture, 

as  indicated  by  the  illuminated  dust, 
is  perfectly  straight.  An  object  is 
seen  by  means  of  light  it  sends  to  the 
eye.  A  small  object  placed  in  a  straight 
line  between  the  eye  and  a  luminous 
point  may  intercept  the  light  in  that 
path,  and  the  point  become  invisible. 
Hence,  we  cannot  see  around  a  cor- 
ner, or  through  a  tube  bent  so  that  a 
straight  string  cannot  be  drawn  through 
its  bore. 

§  305.  Ray,  beam,  pencil.  — Any 
line  RR,  Figure  235,  which  pierces  the 
surface  of  a  wave  of  light  ab  perpen- 
dicularly is  called  a  ray  of  light.  It 
is  an  expression  for  the  direction  in 
which  motion  is  propagated,  and  along 
which  the  successive  effects  of  light  occur.  If  the  wave-surface 
a'b1  is  a  plane,  the  rays  RfRf  are  parallel,  and  a  collection  of 
such  rays  is  called  a  beam  of  light.  If  the  wave-surface  a"b" 
is  spherical  or  concave,  the  rays  R"R"  have  a  common  point  at 
the  center  of  curvature,  and  a  collection  of  such  rays  is  called 
a  pencil  of  light. 

§  306.  Transparent,  translucent,  and  opaque  bodies.  — 
Bodies  are  transparent,  translucent,  or  opaque,  according  to  the 
manner  in  which  they  act  upon  the  luminiferous  waves  which 
pass  through  them.  Generally  speaking,  those  objects  are 


LUMINOUS   AND   ILLUMINATED   OBJECTS. 


329 


transparent  that  allow  other  objects  to  be  seen  through  them 
distinctly  ;  e.g.,  air,  glass,  and  water.  Those  objects  are  trans- 
lucent that  allow  light  to  pass,  but  in  such  a  scattered  condition 
that  objects  are  not  seen  distinctly  through  them;  e.g.,  fog, 
ground  glass,  and  oiled  paper.  Those  objects  are  opaque  that 
apparently  cut  off  all  the  light  and  prevent  objects  from  being 
seen  through  them. 

§  307.  Luminous  and  illuminated  objects.  —  Some  bodies 
are  seen  by  means  of  light,  which  they  generate  and  emit ;  e.g., 
the  sun,  a  candle  flame,  and  a  "live  coal";  they  are  called 
luminous  bodies.  Other  bodies  are  seen  only  b}r  means  of  light 
which  they  receive  from  luminous  ones,  and  when  thus  rendered 
visible,  are  said  to  be  illuminated;  e.g.,  the  moon,  a  man,  a 
cloud,  and  a  "dead"  coal. 

§  308.  Every  point  of  a  luminous  body  an  independent 
source  of  light.  —  Place  a  caudle  flame  in  the  center  of  a 
darkened  room ;  every  wall  and 
every  point  of  each  wall  becomes 
illuminated.  Place  your  eye  in 
any  part  of  the  room,  i.e.,  in  any 
direction  from  the  flame  ;  it  is  able 
to  see  not  only  the  flame,  but 
every  point  of  the  flame  ;  hence 
every  point  of  the  flame  must  emit 
light  in  every  direction.  Every 
point  of  a  luminous  body  is  an  in- 
dependent source  of  light  and  emits 
light  in  every  direction.  Such  a 
point  is  called  a  luminous  point.  In  Figure  236  there  are 
represented  a  few  of  the  infinite  number  of  pencils  of  light 
emitted  by  three  luminous  points  of  a  candle  flame.  Every  point 
of  an  illuminated  object  ab  receives  light  from  every  luminous 
point. 


Fig.  236. 


330  RADIANT  ENERGY. — LIGHT. 

§  309.  Images  formed  through  small  apertures.— Ex- 
periment. —  Cut  a  hole  about  8cm  square  in  one  side  of  a  box ;  cover 
the  hole  with  tin-foil,  and  prick  a  hole  in  the  foil  with  a  pin.  Place  the 
box  in  a  darkened  room,  and  a  candle  flame  in  the  box  near  to  the  pin- 
hole.  Hold  an  oiled-paper  screen  before  the  hole  in  the  foil;  an 
inverted  image  of  the  candle  flame  will  appear  upon  the  translucent 
paper.  An  image  is  a  kind  of  picture  of  an  object. 

If  light  from  objects  illuminated  by  the  sun  —  e.g.,  trees, 
houses,  clouds,  or  even  an  entire  landscape  —  is  allowed  to  pass 
through  a  small  aperture  in  a  window  shutter  and  strike  a 
white  screen,  or  a  white  wall  in  a  dark  room,  rays  carrying  with 
them  the  color  of  the  points  from  which  they  issue  will  imprint 
their  own  color  on  the  screen,  and  inverted  images  of  the  objects 
in  their  true  colors  will  appear  upon  it.  The  cause  of  these  phe- 
Fig  237  nomena  is  easily  understood. 

When  no  screen  intervenes 
between  the  candle  and  the 
screen  A,  Figure  237,  every 
point  of  the  screen  receives 
light  from  every  point  of 
the  candle  ;  consequently,  on 
every  point  on  A,  images  of 
the  infinite  number  of  points 
of  the  candle  are  formed. 
The  result  of  the  confusion  of  images  is  equivalent  to  no  image. 
But  let  the  screen  B,  containing  a  small  hole,  be  interposed  ;  then, 
since  light  travels  only  in  straight  lines,  the  point  Y'  can  only 
receive  an  image  of  the  point  Y,  the  point  Z'  only  of  the  point 
Z,  and  so  for  intermediate  points  ;  hence  a  distinct  image  of  the 
object  must  be  formed  on  the  screen  A.  That  an  image  may  be 
distinct,  the  rays  from  different  points  of  the  object  must  not  mix 
on  the  image,  but  all  rays  from  each  point  on  the  object  must 
be  carried  to  its  own  point  on  the  image. 


SHADOWS.  331 

QUESTIONS. 

1.  Why  are  images,  formed  through  apertures,  inverted? 

2.  Why  is  the  size  of  the  image  dependent  on  the  distance  of  the 
screen  from  the  aperture? 

3.  Obtain  the  dimensions,  respectively,  of  an  object  and  its  image, 
and  their  respective  distances  from  the  intervening  screen,  and  ascer- 
tain the  law  that  determines  in  all  cases  the  size  of  an  image. 

4.  Why  does  an  image  become  dimmer  as  it  becomes  larger? 

5.  Why  do  we  not  imprint  an  image  of  our  person  on  every  object 
in  front  of  which  we  stand? 

6.  Can  rays  of  light  cross  one  another  without  interfering? 

7.  What  fact  does  a  gunner  recognize  in  taking  sight? 


§  310.  Shadows.  —  Experiment  1.  Procure  two  pieces  of  tin 
or  card-board,  one  18cm  square,  the  other  3cm  square.  Place  the  first 
between  a  white  wall  and  a  candle  flame  in  a  darkened  room.  The 
opaque  tin  intercepts  the  light  that  strikes  it,  and  thereby  excludes 
light  from  a  space  behind  it. 

This  space  is  called  a  shadow.  That  portion  of  the  surface 
of  the  wall  that  is  darkened  is  a  section  of  the  shadow,  and 
represents  the  form  of  a  section  of  the  body  that  intercepts  the 
light.  A  section  of  a  shadow  is  frequently  for  convenience 
called  a  shadow.  Notice  that  the  shadow  is  made  up  of  two 
distinct  parts,  —  a  dark  center  bordered  on  all  sides  by  a  much 
lighter  fringe.  The  dark  center  is  called  the  umbra,  and  the 
lighter  envelope  is  called  the  penumbra.  . 

Experiment  2.  Carry  the  tin  nearer  the  wall,  and  notice  that  the 
penumbra  gradually  disappears  and  the  outline  of  the  umbra  becomes 
more  distinct.  Employ  two  candle  flames,  a  little  distance  apart,  and 
notice  that  two  shadows  are  produced.  Move  the  tin  toward  the  wall, 
and  the  two  shadows  approach  one  another,  then  touch,  and  finally  over- 
lap. Notice  that  where  they  overlap  the  shadow  is  deepest.  This  part 
gets  no  light  from  either  flame  and  is  the  umbra ;  while  the  remaining 
portion  gets  light  from  one  or  the  other  and  is  the  penumbra. 

Just  so  the  umbra  of  every  shadow  is  the  part  that  gets  no 
light  from  a  luminous  body,  while  the  penumbra  is  the  part 


832 


RADIANT   ENERGY.  —  LIGHT. 


that  gets  light  from  some  portion  of  the  body,  but  not  from 
the  whole. 

Experiment  3.     Repeat    the  above  experiments,   employing  the 
smaller  piece  of  tin,  and  note  all  differences  in  phenomena  that  occur. 

Hold  a  hair  in  the  sunlight,  about  a 
centimeter  in  front  of  a  fly-leaf  of  this 
book,  and  observe  the  shadow  cast  by 
the  hair.  Then  gradually  increase  the 
distance  between  the  hair  and  the  leaf, 
and  note  the  change  of  phenomena.  If 
the  source  of  light  were  a  single  luminous  point,  as  A,  Figure  238,  the 
shadow  of  an  opaque  body  B  would  be  of  infinite  length,  and  would  con- 
sist only  of  an  umbra.  But,  if  the  source  of  light  has  a  sensible  size, 
the  opaque  body  will  intercept  just  as  many  separate  pencils  of  light  as 
there  are  luminous  points,  and  consequently  will  cast  an  equal  number 
of  independent  shadows. 

Fig.  239. 


Let  AB,  Figure  239,  represent  a  luminous  body,  and  CD  an  opaque 
body.  The  pencil  from  the  luminous  point  A  will  be  intercepted  be- 
tween the  lines  C  F  and  D  G,  and  the  pencil  from  B  will  be  intercepted 
between  the  lines  C  E  and  D  F.  Hence,  the  light  will  be  wholly  ex- 
cluded only  from  the  space  between  the  lines  CF  and  DF,  which 
enclose  the  umbra.  The  enveloping  penumbra,  a  section  of  which  is 
included  between  the  lines  CE  and  CF,  and  between  DF  and  D  G, 
receives  light  from  certain  points  of  the  luminous  body,  but  not  from  all. 


LAW  OF   INVERSE   SQUARES.  333 

QUESTIONS. 

1.  Explain  the  umbra  and  penumbra  cast  by  the  opaque  body  H  I, 
Figure  239. 

2.  When  will  a  transverse  section  of  an  umbra  of  an  opaque  body  be 
larger  than  the  object  itself? 

3.  When  has  an  umbra  a  limited  length? 

4.  What  is  the  shape  of  the  umbra  cast  by  the  sphere  C  D,  Figure  239  ? 

5.  If  C  D  should  become  the  luminous  body,  and  A  B  a  non-luminous 
opaque  body,  what  changes  would  occur  in  the  umbra  and  the  shadow 
cast? 

6.  Why  is  it  difficult  to  determine  the  exact  point  where  the  umbra 
of  a  church-steeple  terminates  on  the  ground? 

7.  What  is  the  shape  of  a  section  of  a  shadow  cast  by  a  circular  disk 
placed  obliquely  between  a  luminous  body  and  a  screen?    What  is  its 
shape  when  the  disk  is  placed  edgewise? 

8.  The  section  of  the  earth's  umbra  on  the  moon  in  an  eclipse  always 
has  a  circular  outline.     What  does  this  show  respecting  the  shape  of 
the  earth? 

LI.     PHOTOMETRY. 

§  311.  Law  of  inverse  squares.  — Experiment  1.  Arrange 
apparatus  as  follows :  Lay  a  silver  half-dollar  on  the  center  of  a  circu- 
lar piece  of  stiff,  white,  unglazed  paper  of  15cm  diameter,  and  rub  the 
entire  surface,  except  the  portion  covered  by  the  coin,  with  a  sperm  or 
a  tallow  candle.  Hold  the  paper  in  a  warm  oven  for  a  minute.  When 
the  paper  is  placed  between  two  lights  in  a  darkened  room,  the  un- 
greased  spot  will  appear  light  on  a  dark  background  on  the  side  which 
receives  the  more  light,  and 
dark  on  a  light  background 
on  the  side  which  receives 
less  light ;  but  the  spot  be- 
comes nearly  invisible 
when  both  sides  are  equal- 
ly illuminated.  Draw  a 
straight  chalk  line  across 
a  table,  and  place  at  right 
angles  to  this  line  a  row  of  four  lighted  candles,  and  on  the  same 
line,  at  a  distance,  a  single  lighted  candle.  Half-way  between  this 
candle  and  the  row  of  candles  place  the  prepared  paper,  as  in  Figure 
240.  It  is  evident  that  one  side  of  the  paper  receives  four  times  the 


334  RADIANT    ENERGY. — LIGHT. 

light  that  the  other  does.  Move  the  row  of  lights  slowly  away  from 
the  paper,  or  move  the  single  light  toward  the  paper,  and  a  point  will 
be  found  in  either  case  where  the  spot  will  nearly  disappear.  When 
this  occurs  it  will  be  found  that  the  row  of  lights  is  twice  as  far  from 
the  paper  as  the  single  light.  The  paper  now  receives  the  same  amount 
of  light  from  the  single  light  as  from  the  four  lights. 

Thus,  by  doubling  the  distance,  the  intensity  of  illumination 
is  diminished  four- fold.  In  a  similar  manner  it  may  be  shown 
that  at  three  times  the  distance  it  takes  nine  lights  to  be  equiv- 
alent to  one  light.  Hence,  the  intensity  of  light  diminishes  as 
the  square  of  the  distance  increases.  This  is  called  the  law  of 
inverse  squares. 

Experiment  2.  Introduce  the  paper  disk,  as  above,  between  a 
candle  light  and  a  kerosene  light  or  a  gas  flame,  and  so  regulate  the 
distance  that  the  central  spot  will  disappear,  and  calculate  the  relative 
intensities  of  the  two  lights  in  accordance  with  the  law  of  inverse 
squares. 

Apparatus  arranged  for  this  purpose  is  called  a  photometer. 
' '  The  candle  power,  which  is  the  unit  of  light  generally  em- 
ployed in  photometry,  is  the  amount  of  light  given  by  a  sperm 
candle  weighing  one-sixth  of  a  pound,  and  burning  one  hundred 
and  twenty  grains  an  hour."  The  relative  brightness  of  the  com- 
mon sources  of  light  are  approximately  as  follows l :  — 

Sunlight  at  the  sun's  surface 190,000  candle  power. 

Most  powerful  electric  arc 55,900       "          " 

Most  powerful  calcium  light 1,300       " 

Light  of  ordinary  gas-burner 12  to  16       "          " 

Standard  candle 1       "          " 

4 '  The  total  quantity  of  light  emitted  by  the  sun  is  equivalent 
to  the  light  of  6,300,000,000,000,000,000,000,000,000  (six  thou- 
sand three  hundred  billions  of  billions)  candles."  Of  this  enor- 
mous quantity  of  light  the  earth  intercepts  an  extremely  small 
fraction. 

i  C.  A.  Young. 


VISUAL  ANGLE.  385 

QUESTIONS. 

1.  Suppose  that  a  lighted  candle  is  placed  in  the  center  of  each  of 
three  cubical  rooms  respectively  10,  20,  and  30  feet  on  a  side ;  would  a 
single  wall  of  the  first  room  receive  more  or  less  light  than  a  single 
wall  of  either  of  the  other  rooms? 

%:  Would  one  square  foot  of  a  wall  of  the  third  room  receive  as 
much  light  as  would  be  received  by  one  square  foot  of  a  wall  of  the 
first  room?  If  not,  what  difference  would  there  be,  and  why  the  differ- 
ence? 

3.  If  a  board  10cra  square  is  placed  25cm  from  a  candle  flame,  the  area 
of  the  shadow  of  the  board  cast  on  a  screen  75cm  distant  from  the 
candle  will  be  how  many  times  the  area  of  the  board?    Then  the  light 
intercepted  by  the  board  will  illuminate  how  much  of  the  surface  of 
the  screen  if  the  board  is  withdrawn? 

4.  Give  a  reason  for  the  law  of  Inverse  Squares. 

5.  To  what  besides  light  has  this  law  been  found  applicable? 

6.  The  two  sides  of  a  paper  disk  are  illuminated  equally  by  a  candle 
flame  50cm  distant  on  one  side  and  a  gas  flame  200cm  distant  on  the  other 
side ;  compare  the  intensities  of  the  two  lights  at  equal  distances  from 
their  sources. 

Fig.  241. 


III.     VISUAL  ANGLE,  ETC. 

§312.  Visual  angle. — Experiment.  Prick  a  pin-hole  in  a 
card,  place  an  eye  near  the  hole,  and  look  at  a  pin  about  20cm  distant, 
Then  bring  the  pin  slowly  toward  the  eye,  and  the  dimensions  of  the 
pin  will  appear  to  increase  as  the  distance  diminishes. 

Why  is  this  ?  We  see  an  object  by  means  of  its  image  formed 
on  the  retina  of  the  eye,  and  its  apparent  magnitude  is  deter- 
mined by  the  extent  of  the  retina  covered  by  its  image.  Rays 


336  RADIANT   ENERGY.  —  LIGHT. 

proceeding  from  opposite  extremities  of  an  object,  as  AB,  Fig- 
ure 241,  meet  and  cross  one  another  in  the  window  of  the  eye, 
usually  called  the  pupil.  Now,  as  the  distance  between  the 
points  of  the  blades  of  a  pair  of  scissors  depends  upon  the 
angle  that  the  handles  form  with  one  another,  so  the  size  of  the 
image  formed  on  the  retina  depends  upon  the  size  of  the  angle, 
called  the  visual  angle,  formed  by  these  rays  as  they  enter  the 
eye.  But  the  size  of  the  visual  angle  diminishes  as  the  distance 
of  the  object  from  the  eye  increases,  as  shown  in  the  diagram ; 
e.g.,  at  twice  the  distance  the  angle  is  one-half  as  great,  at 
three  times  the  distance  the  angle  is  one- third  as  great,  and  so 
on.  Hence,  the  apparent  size  of  an  object  diminishes  as  its  dis- 
tance from  the  eye  increases. 


QUESTIONS. 

1.  Why  do  the  rails  of  a  railroad  track  appear  to  converge  as  their 
distance  from  the  observer  increases? 

2.  Why,  in  looking  through  a  long  hall  or  tunnel,  do  the  floor  and 
the  ceiling  appear  to  approach  one  another? 

3.  Why  do  parallel  lines,  retreating  from  the  eye,  appearto  converge? 

4.  Why  can  a  book,  held  in  front  of  the  face,  entirely  conceal  from 
view  a  house? 


§  313.  Methods  of  estimating  size.  —  Let  a  man  stand  beside 
a  boy  of  half  his  hight,  and  to  an  observer,  twenty  feet  distant,  the  for- 
mer will  subtend  a  visual  angle  twice  as  great  as  the  latter,  and  will 
appear  twice  as  tall.  Then,  let  the  man  move  back  twenty  feet  farther 
from  the  observer,  and  he  and  the  boy  will  then  subtend  equal  angles, 
but  they  will  not  appear  to  be  of  equal  hight,  nor  will  the  man's  hight 
appear  diminished  in  a  very  perceptible  degree.  The  sun  and  the  moon 
are  about  4,000  miles  nearer  to  us  when  they  are  in  the  zenith  than  when 
near  the  horizon,  but  in  the  latter  case  they  appear  much  larger. 
It  makes  a  great  difference  in  the  variation  of  the  apparent  size  of  a 
pin,  as  it  moved  to  and  from  the  eye,  whether  it  is  seen  through  a 
pin-hole  in  a  card  or  whether  the  card  is  removed;  and,  again,  whether 
it  is  seen  with  one  eye  or  both  eyes.  The  fact  is,  that  in  estimating 
the  size  of  objects,  our  judgment  is  influenced  by  many  other  things 


VELOCITY    OF    LIGHT.  337 

besides  the  visual  angles  which  they  subtend.  Our  knowledge  of  the 
real  size  of  an  object,  also  of  the  fact  that  the  tendency  of  an  increase 
in  distance  is  to  diminish  the  apparent  size  of  a  body,  and  that  an  ob- 
ject does  not  become  shorter  as  it  moves  away  from  us,  does  much 
toward  correcting  an  estimate  based  on  the  size  of  the  visual  angle. 
Our  estimate  of  the  size  of  objects  whose  size  is  unknown  is  influ- 
enced much  by  comparison  with  objects  in  their  vicinity  whose  size 
is  known,  as  in  the  case  of  the  sun  and  the  moon  when  they  are  in 
range  with  other  objects  in  the  horizon,  and  in  the  case  of  the  pin, 
whether  it  is  seen  alone  through  a  hole  or  in  conjunction  with  other 
objects.  Again,  when  we  look  at  an  object  with  both  eyes  we  are 
obliged  to  turn  the  eyes  inward  or  outward,  according  as  an  object 
approaches  or  recedes,  in  order  that  light  from  the  object  may  continue 
to  enter  the  eye.  The  effort  necessary  to  adapt  the  position  of  the  eyes, 
so  as  to  see  objects  at  different  distances,  helps  in  forming  a  correct 
estimate  of  their  size.  Hence,  the  pin  seen  by  both  eyes  does  not 
appear  to  undergo  so  great  a  change  in  size,  as  it  moves  to  and  from 
the  observer,  as  when  seen  by  one  eye.  We  are  not  at  the  time  con- 
scious of  going  through  the  processes  of  reasoning  indicated  above, 
because  it  has  become  a  matter  of  habit  with  us.  If  a  man  born  blind 
suddenly  acquires  the  power  of  seeing,  he  at  first  makes  ludicrous 
mistakes  in  judging  of  size  and  distance  of  objects,  because  he  has  not 
acquired  these  methods  of  reasoning.  An  infant  will  reach  out  its 
hands  to  seize  a  bird  that  may  be  flying  many  yards  above. 

§  314.  Velocity  of  Light.  —  We  must  believe  that  light- 
waves require  time  to  traverse  space,  although  their  speed  is 
so  great  that  no  ordinary  means  can  measure  the  time,  it  is 
so  short.  But  the  distances  of  the  heavenly  bodies  are  so  great 
that  the  time  that  their  light  requires  to  reach  us  may  be  easily 
measured. 

To  illustrate  one  method,  let  J,  in  Figure  242,  represent  a  clock 
striking  a  single  stroke  every  hour,  and  the  circle  E  E'  a  road  around 
which  a  person  W  travels ;  the  length  of  the  straight  line  E  E'  is  four 
miles.  So  long  as  W  remains  at  E,  the  strokes  come  exactly  once  an 
hour  by  his  watch ;  but,  as  he  moves  away,  the  intervals  become  slightly 
longer,  so  that,  however  long  he  is  on  the  road,  if  the  watch  and  clock 
run  accurately,  when  he  has  reached  E'  the  sound  of  the  bell  reaches 
him  about  twenty  seconds  after  the  hour.  As  he  continues  back  to  E, 


338  RADIANT    ENERGY.  —  LIGHT. 

the  sounds  come  more  and  more  nearly  on  time,  so  that  at  E  they  are 
just  at  the  proper  time.     Similarly,  at  regular  intervals  in  the  heavens 

Flg.  242.  an  ecliPse  of  one 

of  Jupiter's  moons 
takes  place ;  the 
average  interval 
being  known,  add 
it  to  the  time  at 
which  an  eclipse 
is  observed  when 
the  earth  is  near 
E,  and  thus  we  may 
predict  the  times 
of  an  eclipse  for 
years  ahead.  All 
the  eclipses,  ex- 
cept when  the 
earth  is  at  E,  are 
observed  to  be  a 
little  behind  the 
predicted  times ;  at 
E'  as  much  as  16| 

minutes.     But  at  E'  the  light  has  had  to   travel  184,000,000  miles 

farther  to  reach  the  eye  than  at  E. 

Hence,  light  must  travel  at  the  rate  of  184,000,000 -s-(16£  X  60) 
=  about  186,000  miles  (about  300,000km)  in  a  second. 

Sound  creeps  along  at  the  comparatively  slow  pace  of  about 
one-fifth  of  a  mile  (or  -Jkm)  per  second.  The  former  is  the  ve- 
locity with  which  waves  in  ether  are  transmitted  ;  the  latter,  the 
velocity  with  which  waves  in  air  move  forward.  This  great 
difference  can  be  accounted  for  only  on  the  supposition  that  the 
rarity  and  elasticity  of  ether  are  enormously  greater  than  that  of 
air  (see  page  284). 


OF   REFLECTION.  o39 


LIII.     REFLECTION   OF    LIGHT. 

§  315.  Law  of  reflection.  —  Arrange  apparatus  as  follows : 
AB,  Figure  243,  is  a  board  12cm  square,  having  a  mirror  8cm  square 
fastened  to  one  of  its  sides.  E  is  a  rod  24cm  long  inserted  in  the  board 
close  to  the  middle  of  one  of  the  edges  of  the  mirror,  and  perpendicu- 
lar to  the  surface  of  the  board.  D  F  is  an  arc  of  pasteboard  supported 
by  the  rod.  The  outer  edge  of  the  arc  is  described  by  a  radius  equal 
to  the  length  of  the  rod,  and  is  divided  into  degrees.  Cover  the  open- 
ing orifice  of  the  tube  C  of  the  porte  lumiere  l  with  a  circular  tin  pierced 
in  its  center  by  a  circular  hole  ra,  7mm  in  diameter,  and  admit  a  slender 
beam  of  sunlight  me. 

Experiment.  Place  the  mirror  so  that  the  beam  of  light  may  strike 
it  obliquely,  and  just  graze  the  arc  so  as  to  illuminate  it  at  one  point. 
A  beam  of  light  as  it  approaches  an  object  is  termed  an  incident  beam. 
The  beam,  unable  to  pass  through  the  opaque  silvered  surface  of  the 
mirror,  is  reflected  by  this  surface  obliquely,  but  on  the  opposite  side 
of  the  perpendicular  oc.  A  beam  of  light  after  reflection  is  termed  a 
reflected  beam.  The  spot  of  light  Flg 

on  the  arc  produced  by  the  re- 
flected beam  will  be  found  to  be 
the  same  number  of  degrees  dis- 
tant from  the  perpendicular  as  the 
spot  produced  by  the  incident 
beam.  Hence,  the  angle  nco,  called 
the  angle  of  reflection,  is  equal  to 
the  angle  mco,  called  the  angle  of 
incidence.  Incline  the  mirror  so 
that  the  incident  beam  may  strike 
the  mirror  more  or  less  obliquely, 
and  the  reflected  beam  will  leave 
it  always  at  an  equal  angle.  Ren- 
der the  path  of  the  incident  and 
reflected  beam  luminous  by  introducing  a  cloud  of  smoke  from  touch 

1  Some  means  of  introducing  a  beam  of  sunlight  into  a  darkened  room  is  indispensable 
In  experimenting  with  light.  The  experiments  on  this  subject  will  be  given  on  the  suppo- 
sition that  the  pupil  is  provided  with  means  of  accomplishing  this.  Directions  for  con- 
structing apparatus  suited  to  this  purpose,  usually  called  a  porte  lumttre,  may  be  found 
In  Mayer  and  Barnard's  little  book  on  "Light,"  published  by  D.  Appleton  &  Co.,  New 
York,  and  in  Dolbear's  "  Art  of  Projection,"  published  by  Lee  &  Shepherd,  Boston.  A 
description  of  an  inexpensive  apparatus  devised  by  the  author  may  be  found  in  Section  H 
of  the  Appendix. 


340  KADIANT    ENERGY.  —  LIGHT. 

paper,  and  the  angles  formed  with  the  perpendicular  will  be  quite 
apparent.  Light,  as  well  as  sound,  conforms  to  the  general  law  of  reflec- 
tion. (See  page  118.) 

§  316.  Diffused  light.  —  Experiment  1.  Introduce  a  small  beam 
of  light  into  a  darkened  room,  by  means  of  a  porte  lumiere,  and  place 
in  its  path  a  mirror.  The  light  is  reflected  in  a  definite  direction.  If 
the  eye  is  placed  so  as  to  receive  the  reflected  light,  it  will  see,  not  the 
mirror,  but  the  image  of  the  sun,  and  the  light  will  be  painfully  intense. 
Substitute  for  the  mirror  a  piece  of  unglazed  paper.  The  light  is 
not  reflected  by  the  paper  in  any  definite  direction,  but  is  scattered  in 
every  direction,  illuminating  objects  in  the  vicinity  and  rendering  them 
visible.  Looking  at  the  paper,  you  see,  not  an  image  of  the  sun,  but 
the  paper,  and  you  may  see  it  equally  well  in  all  directions. 

Fig.  244. 


The  dull  surface  of  the  paper  receives  light  in  a  definite  direc- 
tion, but  reflects  it  in  every  direction  ;  in  other  words,  it  scatters 
or  diffuses  the  light.  The  difference  in  the  phenomena  in  the 
two  cases  is  caused  by  the  difference  in  the  smoothness  of  the 
two  reflecting  surfaces.  AB,  Figure  244,  represents  a  smooth 
surface,  like  that  of  glass,  which  reflects  nearly  all  the  rays  of 
light  in  the  same  direction,  because  nearly  all  the  points  of 
reflection  are  in  the  same  plane.  CD  represents  a  surface  of 
paper  having  the  roughness  of  its  surface  greatly  exaggerated. 
The  various  points  of  reflection  are  turned  in  every  possible  direc- 
tion ;  consequently,  light  is  reflected  in  every  direction.  Thus, 
the  dull  surfaces  of  various  objects  around  us  reflect  light  in  all 
directions,  and  are  consequently  visible  from  every  side.  Objects 
rendered  visible  by  reflected  light  are  said  to  be  illuminated. 

By  means  of  regularly  reflected  light  we  see  images  of  objects  in 
mirrors,  but  only  in  definite  directions ;  by  means  of  diffused  light  we 
see  the  mirror  itself  in  every  direction.  Whether  we  see  the  image  of 
the  source  of  the  light  (the  eye  being  situated  so  as  to  receive  the 


BEFLECTION    FROM  PLANE  MIBBOBS.  341 

regularly  reflected  light),  or  the  object  on  which  the  light  falls,  or  both 
at  the  same  time,  depends  largely  upon  the  degree  of  smoothness  pos- 
sessed by  the  object  that  reflects  the  light.  Smooth  surfaces  are 
called  mirrors.  Polished  metals  are  the  best  mirrors.  Surfaces  of 
liquids  at  rest  are  excellent  mirrors.  It  is  sometimes  difficult  to  see  a 
smooth  surface  of  a  pond  surrounded  by  trees  and  overhung  by  clouds, 
as  the  eye  is  occupied  by  the  reflected  images  of  these  objects :  but  a 
faint  breath  of  wind,  slightly  rippling  the  surface,  will  reveal  the  water. 
Experiment  2.  Place  a  basin  of  water  on  a  table,  and  hold  a  candle 
flame  so  that  its  rays  may  form  a  large  angle  with  the  liquid  surface, 
and  notice  the  brightness  of  its  image.  Lower  the  candle  and  the  eye 
so  that  the  incident  and  reflected  rays,  as  nearly  as  possible,  graze  the 
surface  of  the  liquid,  and  notice  how  much  brighter  the  image  be- 
comes. Notice  how  much  brighter  the  varnished  surfaces  of  furni- 
ture appear  when  viewed  very  obliquely,  than  when  seen  by  light 
reflected  less  obliquely.  Also  notice  how  much  more  dazzling  is  the 
light  reflected  from  the  surface  of  a  pond  just  before  the  sun  sets, 
than  at  noon  when  the  sun  is  overhead.  This  is  due  in  part  to  our 
being  at  a  suitable  position  to  observe  it. 

The  amount  of  light  reflected  from  a  smooth  surface  increases 
rapidly  as  the  angle  of  incidence  increases.  Thus,  at  a  perpen- 
dicular incidence,  out  of  1,000  parts  of  light  that  strike  a  sur- 
face of  water,  only  18  parts  are  reflected ;  at  40°,  22  parts  are 
reflected  ;  at  80°,  333  parts  ;  and  at  89^°,  721  parts.  The  above 
is  not  even  approximately  true  of  metals  or  substances  having 
metallic  reflection,  such  as  galena,  etc. 

§  317.  Reflection  from  plane  mirrors;  virtual  images.— 
M  M  (Fig.  245)  represents  a  plane  mirror,  and  A  B  a  pencil  of  diver- 
gent rays  proceeding  from  the  point  A  of  an  object  AH.  Erecting 
perpendiculars  at  the  points  of  incidence,  or  the  points  where  these 
rays  strike  the  mirror,  and  making  the  angles  of  reflection  equal  to 
the  angles  of  incidence,  the  paths  BC  and  EC  of  the  reflected  rays 
are  found. 

It  appears  that  divergent  incident  rays  remain  divergent  after 
reflection  from  a  plane  mirror.  In  like  manner  construct  a 
diagram,  and  show  that  parallel  incident  rays  are  parallel  after 
reflection.  Construct  another  diagram,  and  show  that  convergent 


342  RADIANT    ENERGY.  —  LIGHT. 

incident  rays  are  convergent  after  reflection.     To  an  eye  placed 
at  C,  the  points  from  which  the  rays  appear  to  come  are  of  course 
R  in  the  direction  of  the  rays  as  they 

enter  the  eye.  These  points  may  be 
found  by  continuing  the  rays  C  B  and 
CE  behind  the  mirror,  till  they  meet 
at  the  points  D  and  N.  Every  point 
of  the  object  AH  sends  out  its  pen- 
cils of  rays,  and  those  that  strike 
the  mirror  at  a  suitable  angle  to  be 
reflected  to  the  eye,  produce  on  the 
retina  of  the  eye  an  image  of  that 
point,  and  the  point  from  which  the 
light  appears  to  emanate  is  found,  as 
previously  described.  Thus,  the  pencils  EC  and  BC  appear  to 
emanate  from  the  points  N  and  D,  and  the  whole  body  of  light 
received  by  the  eye  seems  to  come  from  an  apparent  object  ND, 
behind  the  mirror.  This  apparent  object  is  called  an  image, 
but  as  of  course  there  can  be  no  real  image  formed  there,  it  is 
called  a  virtual  or  an  imaginary  image.  It  will  be  seen,  by 
construction,  that  an  image  in  a  plane  mirror  appears  as  far 
behind  the  mirror  as  the  object  is  in  front  of  it,  and  is  of  the 
same  size  and  shape  as  the  object. 

If  the  mirror  is  vertical,  objects  appear  in  their  proper  relations  to 
the  horizon ;  but,  if  the  mirror  has  any  other  position,  objects  assume 
unnatural  postures.  Thus,  turn  this  book  so  that  the  mirror  MM 
(Fig.  245)  may  represent  a  horizontal  mirror,  and  AH  a  vertical  object 
above  it,  and  it  will  be  seen  that  the  image  appears  inverted.  To 
verify  this,  place  a  mirror  in  a  horizontal  position,  and  set  on  it  a 
goblet  of  water.  Also  show  by  construction  that,  in  a  mirror  making 
an  angle  of  45°  with  the  horzon,  vertical  objects  appear  horizontal  and 
vice  versa.  Verify  this  by  experiment.  Pupils  may  amuse  themselves 
at  their  leisure,  and  at  the  same  time  be  instructed,  by  performing  the 
following  experiments :  — 

Experiment  1.  Place  a  printed  page  in  front  of  a  mirror,  and 
attempt  to  read  the  print  from  the  mirror.  It  will  be  seen  that  there 


MULTIPLE  REFLECTION.  343 

is  always  a  lateral  inversion ;  for  the  same  reason  that  when  two  per- 
sons stand  facing  one  another,  the  right  hand  of  one  is  opposite  the 
left  hand  of  the  other. 

Experiment  2.  Place  two  mirrors  facing  one  another  and  about  15cra 
apart.  Hold  a  pencil  half-way  between  the  mirrors,  and  look  obliquely 
into  one  mirror  just  over  the  edge  of  the  other,  and  you  will  see  § 
large  number  of  images  of  the  pencil  arranged  at  equal  distances 
behind  one  another.  Account  for  these  images. 

Experiment  3.  Place  two  mirrors  edge  to  edge  so  as  to  form  an 
angle  of  45°  with  one  another.  Place  the  face  in  the  opening,  and 
gradually  close  the  mirrors  till  they  touch  the  head. 

§  318.  Multiple  reflection.  —  Experiment  l.  Allow  the 
beam  of  light  in  the  last  experiment  to  strike  a  wall  of  the  room. 
There  will  be  projected  upon  the  wall  two,  and  perhaps  more,  circular 
images  of  the  sun  overlapping  one  auother.  It  appears  as  though  the 
beam  of  light  is  somehow  split,  by  re-  Fig.  246. 

flection  from  the  mirror,  into  two  or 
more  parts,  and  that  these  parts  travel 
thereafter  in  slightly  different  paths. 

Experiment  2.  Hold  a  candle  flame 
in  such  a  position  (Fig.  246)  that  its 
light  may  strike  a  mirror  (one  having 
very  thick  glass  is  best)  very  obliquely, 
and  place  the  eye  so  that  it  may  receive 
the  reflected  light,  and  you  may  see 
many  images  of  the  flame. 

Experiment  3.     Place  a  pencil  per- 
pendicular to  a  mirror,   with   the  point 
touching  the  glass,  and  you  will  see  two 
images  of  the  pencil,  —  one  touching  the  point  of  the  pencil,  and  the 
other  at  a  distance  equal  to  twice  the  thickness  of  the  glass. 

How  are  these  phenomena  produced?  As  you  travel  the 
sidewalk  and  pass  windows,  you  frequently  see  your  own  image 
and  images  of  other  outdoor  objects  reflected  by  the  glass, 
showing  that  even  so  transparent  a  substance  as  glass  does  not 
allow  all  the  light  that  strikes  it  to  pass  through  it,  but  reflects 
a  portion.  Let  a  beam  of  light  Aa,  Figure  247,  strike  a  mirror 
B  C  obliquely  ;  n,  portion  of  the  light  is  reflected  from  the  point 


344  RADIANT    ENERGY.  —  LIGHT. 

of  incidence  a,  and  strikes  the  screen  D  E  at  5.  Another  por- 
tion of  the  light  enters  the  glass,  and  a  portion  of  it  is  reflected 
from  the  point  c,  and  a  portion  of  this  last  reflected  light  strikes 
the  screen  at  d,  while  the  remainder  is  reflected  from  e  to  /, 
and  again  from  /,  and  a  portion  of  it  reaches  the  screen  at  0, 
Fig<  247.  while  the  remainder 

is  reflected  from  h 
to  i,  and  undergoes 
further  reflections 
and  splittings,  until 
the  light,  in  conse- 
quence of  the  loss 
occasioned  by  suc- 
cessive divisions, 
becomes  too  feeble 
to  produce  distinct 
effects.  If  the  eye 
take  the  place  of  the  screen,  since  an  object  is  seen  in  the  direc- 
tion in  which  the  light  comes  to  the  eye,  the  point  A  will  appear 
to  lie  somewhere  on  the  line  &a,  extended ;  for  the  same  reason 
it  will  appear  to  lie  on  the  lines  de,  gh,  etc. ;  but  as  these  lines 

have  no  point  in  com- 
mon, it  is  clear  that 
the  effect  would  be  that 
of  multiple  images. 
(Show  the  application 
of  this  explanation  in 
accounting  for  the  phe- 
nomena obtained  in  the 
above  experiments.) 

319.  Reflection  from  concave  mirrors.  —  Let  MM', 
Figure  248,  represent  a  section  of  a  concave  mirror,  which  may 
be  regarded  as  a  small  part  of  a  hollow  spherical  shell  having  a 
polished  interior  surface.  The  distance  MMf  is  called  the  aper- 


REFLECTION   FROM   CONCAVE    MlBKOKS.  345 

ture  of  the  mirror.  C  is  the  center  of  the  sphere,  and  is  called 
the  center  of  curvature.  G  is  the  vertex  of  the  mirror.  A 
straight  line  DG,  drawn  through  the  center  of  curvature  and 
the  vertex  is  called  the  principal  axis  of  the  mirror.  A  concave 
mirror  may  be  considered  as  made  up  of  an  infinite  number  of 
small  plane  surfaces.  All  radii  of  the  mirror,  as  CA,  CG,  and 
CB,  are  perpendicular  to  the  small  planes  which  they  strike. 
If  C  be  a  luminous  point,  it  is  evident  that  all  light  emanating 
from  this  point,  and  striking  the  mirror,  will  be  reflected  back  to 
its  source  at  C. 

Let  E  be  any  luminous  point  in  front  of  a  concave  mirror.  To  find 
the  direction  that  rays  emanating  from  this  point  take  after  reflection, 
draw  any  two  lines  from  this  point,  as  EA  and  EB,  representing  two 
of  the  infinite  number  of  rays  composing  the  divergent  pencil  of  light 
that  strikes  the  mirror.  Next  draw  radii  to  the  points  of  incidence  A 
and  B,  and  draw  the  lines  AF  and  BF,  making  the  angles  of  reflection 
equal  to  the  angles  of  incidence.  Place  arrow-heads  on  the  lines  rep- 
resenting rays  of  light  to  indicate  the  direction  of  the  motion.  The 
lines  AF  and  BF  represent  the  direction  of  the  rays  after  reflection. 

It  will  be  seen  that  the  rays  after  reflection  are  convergent, 
and  meet  at  the  point  F,  called  the  focus.  This  point  is  the 
focus  of  all  reflected  rays  that  emanate  from  the  point  E.  It 
is  obvious  that  if  F  were  the  luminous  point,  the  lines  AE 
and  BE  would  represent  the  reflected  rays,  and  E  would  be 
the  focus  of  these  ra}*s.  Since  the  relation  between  two  such 
points  is  such  that  light  emanating  from  either  one  is  brought 
by  reflection  to  a  focus  at  the  other,  they  are  called  conju- 
gate foci.  Conjugate  foci  are  two  points  so  related  that  the 
image  of  one  is  formed  at  the  other.  The  rays  EA  and  EB 
emanating  from  E  are  less  divergent  than  rays  FA  and  FB, 
emanating  from  a  point  F  less  distant  from  the  mirror,  and 
striking  the  same  points.  Rays  emanating  from  D,  and  striking 
the  same  points  A  and  B,  will  be  still  less  divergent ;  and  if  the 
point  D  were  removed  to  a  distance  of  many  miles,  the  rays 
incident  at  these  points  would  be  very  nearly  parallel.  Hence 


346  11ADIANT    ENERGY.  —  LIGHT. 

rays  may  be  regarded  as  practically  parallel  when  their  source 
is  at  a  very  great  distance,  e.g.,  the  sun's  rays.  If  a  sunbeam, 
consisting  of  a  bundle  of  parallel  rays,  as  E  A,  D  Gr,  and  H  B 
(Fig.  249),  strike  a  concave  mirror  parallel  with  its  principal 
m  ^  axis,  they  become  convergent  by  reflection, 

and  meet  at  a  point  (F)  in  the  principal  axis. 
This  point,  called  the  principal  focus,  is  just 
half-way  between  the  center  of  curvature  and 
the  vertex  of  the  mirror. 

On  the  other  hand,  it  is  obvious  that  diver- 
gent rays  emanating  from  the  principal  focus 
of  a  concave  mirror  become  parallel  by  reflection. 

If  a  small  piece  of  paper  is  placed  at  the  principal  focus  of  a 
concave  mirror,  and  the  mirror  is  exposed  to  the  parallel  rays 
of  the  sun,  the  paper  will  quickly  burn,  showing  that  the  focus 
of  light  is  also  a  focus  of  heat;  or,  in  other  words,  that  all  forms 
of  radiant  energy  follow  the  same  laws  of  reflection  as  light. 

Construct  a  diagram,  and  show  that  rays  of  light  proceed- 
ing from  a  point  between  the  principal  focus  and  the  mirror 
are  divergent  after  reflection,  but  less  divergent  than  the  inci- 
dent rays.  Reversing  the  direction  of  the  light,  the  same  dia- 
gram will  show  that  convergent  rays  of  light  are  rendered  more 
convergent  by  reflection  from  concave  mirrors.  The  general 
effect  of  a  concave  mirror  is  to  increase  the  convergence  or  to  de- 
crease the  divergence  of  incident  rays. 

The  statement,  that  parallel  rays  after  reflection  from  a  concave 
mirror  meet  at  the  principal  focus,  is  only  approximately  true.  The 
smaller  the  aperture  of  the  mirror,  the  more  nearly  true  is  the  state- 
ment. It  is  strictly  true  only  of  parabolic  mirrors,  such  as  are  used 
with  the  head-lights  of  locomotives.  Construct  a  diagram  representing 
a  mirror  of  large  aperture,  and  it  will  be  found  that  those  rays  that 
strike  the  mirror  at  considerable  distance  from  its  center,  intersect  the 
principal  axis  after  reflection  at  points  nearer  to  the  mirror  than  the 
principal  focus. 

§  320.  Formation  of  images. — Experiment  1.  In  a  dark  room 
hold  the  concave  side  of  a  bright  silver  dessert  spoon  a  little  distance 


FORMATION   OF   IMAGES.  347 

in  front  of  the  face,  and  introduce  a  candle  flame  between  the  spoon 
and  your  eyes ;  you  will  see  a  small  inverted  image  of  the  flame  about 
a  centimeter  in  front  of  the  spoon. 

Experiment  2.  Turn  the  convex  side  of  the  spoon  toward  you,  and 
you  will  see  a  small  erect  image  of  the  flame  a  little  back  of  the  spoon. 

Experiment  3.  Repeat  the  two  preceding  experiments,  holding  'the 
spoon  between  the  flame  and  the  eyes,  but  not  so  as  to  screen  the  face 
from  the  light,  and  you  will  see  similar  images  of  yourself. 

To  determine  the  position  and  kind  of  images  formed  of  objects 
placed  in  front  of  concave  mirrors,  proceed  as  follows :  Locate  the 
object,  as  D  E,  Figure  250.    Draw  lines,  E  A  and  DB,  from  the  extrem- 
ities of  the  object  through  the  center  Fig.  250. 
of  curvature  of  the  mirror,  to  meet  the 
mirror.     These  lines  are  called  the  sec- 
ondary axes.    Incident  rays  along  these 
lines  will  return  by  the    same  paths 
after  reflection.    (Why?)   Draw  another 
line  from  D  to  any  point  in  the  mirror, 
e.g.,  to  F,  to  represent  any  other  of  the 
infinite  number  of  rays  emanating  from 
D.     Make  the  angle  of  reflection  CFD'  equal  to  the  angle  of  in- 
cidence CFD,  and  the  reflected  ray  will  intersect  the  secondary  axis 
DB  at  the  point  D'.     This  point  is  the  conjugate  focus  of  all  rays 
proceeding  from  D.    Consequently,  an  image  of  the  point  D  is  formed 
at  D'.   This  image  is  called                                 m    ^ 
a  real  image,  because  rays 
actually  meet  at  this  point. 
In  a  similar  manner,  find  the 
pointE',the  conjugate  focus 
of  the  point  E.   The  images 
of  intermediate  points  be- 
tween D  and  E  lie  between 
the  points  D'  and  E' ;  and, 
consequently,  the  image  of 
the  object  lies  between  those 
points  as  extremities. 

If,  for  the  second  ray  to  be  drawn  from  any  point,  we  select 
that  ray  which  is  parallel  with  the  principal  axis,  as  A  G,  Figure  251,  it 
will  not  be  necessary  to  measure  angles.  For  this  ray,  after  reflec- 
tion, must  pass  through  the  principal  focus  F ;  and  consequently  the 
conjugate  focus  A'  is  easily  found,  and  so  for  the  point  B'  and  inter- 


348  RADIANT    ENERGY. — LIGHT. 

mediate  points.     Both  methods  of  constructing  images  should  be  prae 
tised  by  the  pupil. 

It  thus  appears  that  an  image  of  an  object  placed  beyond  the 
center  of  curvature  of  a  concave  mirror  is  real,  inverted,  smaller 
than  the  object,  and  located  between  the  center  of  curvature  and  the 
principal  focus  of  the  mirror.    An  eye  placed  in  a  suitable  posi- 
tion to  receive  the  light,  as  at 

Fie  252 

H  (Fig.  252),  will  receive  the 
same  impression  from  the  re- 
flected rays  as  if  the  image 
E'  D'  were  a  real  object.  For 
a  cone  of  rays  originally  eman- 
ates from  (say)  the  point  D  of 
the  object,  but  it  enters  the  eye 
as  if  emanating  from  D',  and  consequently  appears  to  originate 
from  the  latter  point.  A  person  standing  in  front  of  such  a 
mirror,  at  a  distance  greater  than  its  radius  of  curvature,  will 
see  an  image  of  himself  suspended,  as  it  were,  in  mid-air.  Or, 
if  in  a  darkened  room  an  illuminated  object  is  placed  in  front  of 
the  miiTor,  and  a  small  oiled-paper  screen  is  placed  where  the 
image  is  formed,  a  large  audience  may  see  the  image  projected 
upon  the  screen. 

If  E'  Df  (Fig.  250)  is  taken  as  the  object,  then  the  direction 

of  the  light  in  the  diagram 
will  be  reversed,  and  ED 
will  represent  the  image. 
Hence,  the  image  of  an  ob- 
ject placed  between  the  prin- 
cipal focus  and  the  center  of 
curvature  is  also  real  and 
inverted,  but  larger  than  the 
object,  and  located  beyond 
the  center  of  curvature.  The  image  in  this  case  may  be  pro- 
jected upon  a  screen,  but  it  will  not  be  so  bright  as  in  the 
former  case,  because  the  light  is  spread  over  a  larger  surface. 


FORMATION   OF   IMAGES.  349 

Construct  the  image  of  an  object  placed  between  the  principal 
focus  and  the  mirror,  as  in  Figure  253.  It  will  be  seen  in  this 
case  that  a  pencil  of  ra}^s  proceeding  from  K  254. 

any  point  of  an  object,  e.g.,  D,  has  no 
actual  focus,  but  appears  to  proceed  from 
a  virtual  focus  D',  back  of  the  mirror,  and 
so  with  other  points,  as  E.  The  image  of 
an  object  placed  between  the  principal  focus 
and  the  mirror  is  virtual,  erect,  larger  than 
the  object,  and  is  back  of  the  mirror. 

QUESTIONS. 

Ascertain  the  answers  to  the  following  questions  by  constructing 
suitable  diagrams,  and  afterwards  verify  your  conclusions  by  experi- 
ment, if  convenient. 

1.  When  an  object  is  located  at  a  distance  from  a  concave  mirror 
equal  to  its  radius,  will  any  image  be  formed?    Why? 

2.  What  is  the  effect  of  placing  the  object  at  the  principal  focus? 
Why? 

3.  (a)  When  is  the  real  image  formed  by  a  concave  mirror  smaller 
than  the  object?    (&)  When  is  it  larger? 

4.  (a)  When  is  the  image  formed  by  a  concave  mirror  real?     (6) 
When  is  it  virtual? 

5.  (a)  Is  the  image  of  an  object  formed  by  a  convex  mirror  real  or 
virtual?     (b)  Is  it  larger  or  smaller  than  the  object?     (c)  Is  it  erect  or 
inverted? 

NOTE.  —  The  diagram  in  Figure  254  will  be  found  sufficiently  sug- 
gestive as  to  the  method  of  finding  the  disposition  of  a  pencil  of  rays 
emanating  from  any  point,  e.g.,  A,  after  reflection  from  a  convex 
mirror. 

6.  Is  the  general  effect  of  a  convex  mirror  to  collect  or  to  scatter 
rays? 


350  RADIANT    ENERGY.  —  LIGHT. 


LIV.     REFRACTION. 

Experiment  1.  Across  the  bottom  of  a  rectangular  tin  basin  ABC 
D,  Figure  255,  mark  a  scale  of  millimeters.     Into  a  darkened  room 
admit  a  beam  of  sunlight,  so  that  its  rays  may  fall  obliquely  on  the 
bottom  of  the  basin,  and  note  the  place  on  the  scale  where  the  edge  of 
p.    255  the  shadow  D  E  cast  by  the  side  of 

the  basin  D  C  meets  the  bottom  at  E. 
Then,  without  moving  the  basin,  fill 
it  even  full  with  water  slightly 
clouded  with  milk,  or  with  a  few 
drops  of  a  solution  of  mastic  in  alco- 
hol. It  will  be  found  that  the  ^dge 
of  the  shadow  has  moved  from  D  E 
to  D  F,  and  meets  the  bottom  at  F. 
Beat  a  blackboard  rubber,  and  create 
a  cloud  of  dust  in  the  path  of  the 
beam  in  the  air,  and  you  will  discover 
that  the  rays  G  D  that  graze  the  edge  of  the  disk  at  D  become  bent 
at  the  point  where  they  enter  the  water,  and  now  move  in  the  bent 
line  GD  F,  instead  of,  as  formerly,  in  the  straight  line  GE.  The  path 
of  the  light  in  the  water  is  now  nearer  to  the  vertical  side  DC; 
in  other  words,  this  part  of  the  beam  is  more  nearly  vertical  than  before. 
Experiment  2.  Place  a  coin  (A,  Fig.  256)  on  the  bottom  of  an 
empty  basin,  so  that,  as  you  look  through  a  small  hole  in  a  card  B  C 
over  the  edge  of  the  vessel,  the  coin  is  just  out  of  sight.  Then,  with- 
out moving  the  card  or  basin,  fill  the  latter  with  water.  Now,  on 
looking  through  the  aperture  in  the  card,  the  coin  is  visible.  The 
beam  of  light  AE,  which  formerly  moved  in  the  straight  line  AD,  is 
now  bent  at  E,  where  it  leaves  the  water,  and,  passing  through  the 
aperture  in  the  card,  enters  the  eye.  Observe 
that,  as  the  light  passes  from  the  water  into 
the  air,  it  is  turned  farther  from  a  vertical  line 
EF;  in  other  words,  the  beam  is  farther  from 
the  vertical  than  before. 

Experiment  3.  From  the  same  position  as 
in  the  last  experiment,  direct  the  eye  to  the 
point  G  in  the  basin  filled  with  water.  Reach 
your  hand  around  the  basin,  and  place  your 
finger  where  that  point  appears  to  be.  On  ex- 
amination, it  will  be  found  that  your  finger  is  considerably  above  the 


CAUSE    OF   REFRACTION.  351 

bottom.  Hence,  the  effect  of  the  bending  of  rays  of  light,  as  they  pass 
obliquely  out  of  water,  is  to  cause  the  bottom  to  appear  more  elevated  than  it 
really  is  ;  in  other  words,  to  cause  the  water  to  appear  shallower  than  it  is. 

Experiment  4.    Thrust  a  pencil  obliquely  into  water,  and  it  will 
appear  shortened,  bent  at  the  surface  of  the  water,  and  the     F.    ^ 
immersed  portion  elevated.  'j 

Experiment  5.    Place  a  piece  of  wire  (Fig.  257)  verti- 
cally in  front  of  the  eye,  and  hold  a  narrow  strip  of  thick 
plate  glass  horizontally  across  the  wire,  so  that  the  light 
from  the  wire  may  pass  obliquely  through  the  glass  to  the 
eye.    The  wire  will  appear  to  be  broken  at  the  two  edges 
of  the  glass,  and  the  intervening  section  will  appear  to  be  moved  to 
the  right  or  left  according  to  the  inclination  of  the  glass ;  but,  if  the 
glass  is  not  inclined  to  the  one  side  or  the  other,  the  wire  does  not 
appear  broken. 

When  a  beam  of  light  passes  from  one  medium  into  another  of 
different  density,  it  is  bent  or  refracted  at  the  boundary  plane 
between  the  two  media,  unless  it  falls  exactly  perpendicularly 
on  this  plane.  If  it  passes  into  a  denser  medium,  it  is  refracted 
toward  a  perpendicular  to  this  plane;  if  into  a  rarer  medium,  it 
is  refracted  from  the  perpen-  Fig.  258. 

dicular.  The  angle  GDO  (Fig. 
255)  is  called  the  angle  of  inci- 
dence; FDN,  the  angle  of  re- 
fraction; and  EDF,  the  angle 
of  deviation. 


.  §  321.  Cause  of  refraction. 
—  Careful  experiments  have 
proved  that  the  velocity  of  light 
is  less  in  a  dense  than  in  a  rare 
medium.  Let  the  series  of  par- 
allel lines  AB  (Fig.  258)  repre- 
sent a  series  of  wave-fronts  leaving  an  object  C,  and  passing 
through  a  rectangular  piece  of  glass  DE,  and  constituting  a 
beam  of  light.  Every  point  in  a  wave-front  moves  with  equal 
velocity  as  long  as  it  traverses  the  same  medium ;  but  the  point 


352 


RADIANT    ENERGY. 


LIGHT. 


a  of  a  given  wave  ab  enters  the  glass  first,  and  its  velocity  is 
impeded,  while  the  point  b  retains  its  original  velocity ;  so 
that,  while  the  point  a  moves  to  a',  b  moves  to  &',  and  the 
result  is  that  the  wave-front  assumes  a  new  direction  (very 
much  in  the  same  manner  as  a  line  of  soldiers  execute  a  wheel) , 
and  a  ray  or  a  line  drawn  perpendicularly  through  the  series  of 
waves  is  turned  out  of  its  original  direction  on  entering  the  glass. 
Again,  the  extremity  c  of  a  given  wave-front  cd  first  emerges 
from  the  glass,  when  its  velocity  is  immediately  quickened ;  so 
that,  while  d  advances  to  d',  c  advances  to  c',  and  the  direction 
of  the  ray  is  again  changed.  The  direction  of  the  ray,  after 
emerging  from  the  glass,  is  parallel  to  its  direction  before  enter- 
ing it,  but  it  has  suffered  a  lateral  displacement.  Let  C  repre- 
sent a  section  of  the  wire  used  in  Exp.  5,  and  the  cause  of 
the  phenomenon  observed  will  be  apparent.  If  the  beam  of 
light  strikes  the  glass  perpendicularly,  all  points  of  the  wave 
will  be  checked  at  the  same  instant  on  entering  the  glass  ;  con- 
sequently it  will  suffer  no  refraction. 

§  322.  Index  of  refraction.  —  The  deviation  of  light,  in 

passing  from  one  medium  to 
another,  varies  with  the  me- 
dium and  with  the  angle  of 
incidence.  It  diminishes  as 
the  angle  of  incidence  dimin- 
ishes, and  is  zero  when  the 
incident  ray  is  normal  (i.e., 
perpendicular  to  the  surface 
of  the  medium) .  It  is  highly 
important ,  knowing  the  angle 
of  incidence,  to  be  able  to 
determine  the  direction 
which  a  ray  of  light  will  take 
on  entering  a  new  medium.  Describe  a  circle  around  the  point 
of  incidence  A  (Fig.  259)  as  a  center,  with  a  radius  of  (say) 


Fig.  259. 


INDICES    OF    REFRACTION. 


353 


10cm  ;  through  the  same  point  draw  IH  perpendicular  to  the 
surfaces  of  the  two  media,  and  to  this  line  drop  perpendiculars 
BD  and  CE  from  the  points  where  the  circle  cuts  the  ray  in  the 
two  media.  Then  suppose  that  the  perpendicular  B  D  is  y8^  of 
the  radius  A  B  ;  now  this  fraction  y8^  is  called  (in  Trigonom- 
etry) the  sine  of  the  angle  DAB.  Hence,  y8^  is  the  sine  of 
the  angle  of  incidence.  Again,  if  we  suppose  that  the  perpen- 
dicular C  E  is  T%  of  the  radius,  then  the  fraction  y6^  is  the 
sine  of  the  angle  of  refraction.  The  sines  of  the  two  angles 
are  to  one  another  as  T8^  :  y6^,  or  as  4  :  3.  The  quotient  (in  this 
case  |)  obtained  by  dividing  the  sine  of  the  angle  of  incidence 
by  the  sine  of  the  angle  of  refraction  is  called  the  index  of  refrac- 
tion. It  can  be  proved  to  be  the  ratio  of  the  velocity  of  the 
incident  to  that  of  the  refracted  light.  It  is  found  that,  for  the 
same  media  the  index  of  refraction  is  a  constant  quantity;  i.e., 
the  incident  ray  might  be  more  or  less  oblique,  still  the  quotient 
would  be  the  same. 

§  323.  Indices  of  refraction.  —  The  index  of  refraction  for 
light  in  passing  from  air  into  water  is  approximately  f ,  and 
from  air  into  glass  f  ;  and,  of  course,  if  the  order  is  reversed,  the 
reciprocal  of  these  fractions  must  be  taken  as  the  indices  ;  e.g., 
xTom  water  into  air  the  index  is  J,  from  glass  into  air  ^.  When 
a  ray  passes  from  a  vacuum  into  a  medium,  the  refractive  index 
is  greater  than  unity,  and  is  called  the  absolute  index  of  refrac- 
tion. The  relative  index  of  refraction,  from' any  medium  A  into 
another  B,  is  found  by  dividing  the  absolute  index  of  B  by  the 
absolute  index  of  A. 

The  refractive  index  varies  with  the  color  of  the  light.  (See 
page  365.)  The  following  table  is  intended  to  represent  mean 
indices :  — 

TABLE  OF  ABSOLUTE  INDICES. 


Air  at  0°  C.  and  760mm  pressure  .  1.000294 

Pure  water 1.33 

Alcohol 1.37 

Spirits  of  turpentine 1.48 

Humors  of  the  eye  (about)      .     .  1.35 


Carbon  bisulphide 1.641 

Crown  glass  (about) 1.53 

Flint  glass  (about) .  1.61 

Diamond  (about) 2.5 

Lead  chromate 2.97 


354  RADIANT    ENERGY.  —  LIGHT. 


EXERCISES. 

1.  Draw  a  straight  line  to  represent  a  surface  of  flint  glass,  and 
draw  another  line  meeting  this  obliquely  to  represent  a  ray  of  light 
passing  from  a  vacuum  into  this  medium.     Find  the  direction  of  the 
ray  after  it  enters  the  medium,  employing  the  index  as  given  in  the 
above  table. 

2.  (a)  Determine  the  index  of  refraction  for  light  in  passing  from 
water  into  diamond.     (&)  In  passing  from  water  into  air. 

3.  Ascertain  the  index  of  refraction  for  water  in  Exp.  1,  p.  350,  in 

E  C 
which  sine  I  (sine  of  angle  of  incidence)  =  — -    (Fig.  255),  and  sine 

F  C  -fill 

R  (sine  of  angle  of  refraction)  =  — — .     Hence,  the  index  of  refraction 

_  sine  I  =  E  C    .  F  C 
sine  R     E  D  '  F  D 

Fig.  260. 


§  324.  Critical  angle;  total  reflection.  —  Let  SS'  (Fig. 
2 GO),  represent  the  boundar}T-surface  between  two  media,  and 
AO  and  BO  incident  rays  in  the  more  refractive  medium  (e.g., 
glass)  ;  then  OD  and  OE  may  represent  the  same  rays  respec- 
tively after  they  enter  the  less  refractive  medium  (e.g.,  air). 
It  will  be  seen  that,  as  the  angle  of  incidence  is  increased,  the 
refracted  ray  rapidly  approaches  the  surface  OS.  Now,  there 
must  be  an  angle  of  incidence  (e.g.,  COM)  xuch  that  the  angle 


REFRACTION   AND   TOTAL  REFLECTION.  355 

of  refraction  will  be  90° ;  in  this  case  the  incident  ray  CO,  after 
refraction,  will  just  graze  the  surface  OS.  This  is  called  the 
critical  or  limiting  angle.  Any  incident  ray,  as  LO,  making  a 
larger  angle  with  the  normal  than  the  critical  angle,  cannot 
emerge  from  the  medium,  and  consequently  is  not  refracted. 
Experiment  shows  that  all  such  rays  undergo  internal  reflection, 
e.g.,  the  ray  LO  is  reflected  in  the  direction  ON.  Reflection  in 
this  case  is  perfect,  and  hence  is  called  total  reflection.  Total 
reflection  occurs  tvhen  rays  in  the  more  refractive  medium  are  in- 
cident at  an  angle  greater  than  the  critical  angle.  Surfaces  of 
transparent  media,  under  these  circumstances,  constitute  the 
best  mirrors  possible.  The  critical  angle  diminishes  as  the  re- 
fractive index  increases.  For  water  it  is  about  48^°  ;  for  flint 
glass,  38°  41 f;  and  for  diamond,  23°  41'.  Light  cannot,  there- 
fore, pass  out  of  water  into  air  with  a  greater  angle  of  incidence 
than  48 y.  The  brilliancy  of  gems,  particularly  the  diamond, 
is  due  in  part  to  their  extraordinary  power  of  internal  reflection. 
It  is  evident  that  all  incident  light  embraced  in  the  angular 
space  KOS,  not  reflected  at  the  surface,  is  condensed  by  refrac- 
tion into  the  angular  space  COM  of  48^°,  or  that  the  whole 
light  that  passes  into  the  water  is  condensed  into  an  angular 
space  of  97°.  A  diver,  looking  upward,  can  see  external  ob- 
jects, as  it  were,  only  through  a  circular  aperture  overhead  of 
limited  diameter ;  while  beyond  this  circle  he  sees,  as  the  effect 
of  total  reflection,  the  various  objects  on  the  bottom. 

§  325.  Illustrations  of  refraction  and  total  reflection.  — 

Experiment  1.  Place  a  bright  coin  in  a  tumbler  of  water,  and  tilt  the 

glass  till  the  light  from  the  coin  strikes  the  surface  of  the  water  above 

with  sufficient  obliquity,  so  that,  looking  upward  toward  that  surface, 

you  can  see  there  a  distinct  image  of  the  coin. 

Experiment  2.  Thrust  the  closed  end  of  a  glass  test-tube  into 
water,  and  incline  the  tube.  Look  down  upon  the  immersed  part  of 
the  tube,  and  its  upper  surface  will  look  like  burnished  silver,  or  as  if 
the  tube  contained  mercury.  Fill  the  test-tube  with  water,  and  immerse 
as  before ;  the  total  reflection  which  before  occurred  at  the  surface  of 
the  air  in  the  submerged  tube  now  disappears.  Explain. 


356 


RADIANT    ENERGY.  —  LIGHT. 


Fig.  261. 


Experiment  3.  Place  uncolored  glass  beads,  or  glass  broken  into 
quite  small  pieces,  in  a  test-tube.  They  appear  not  only  white,  due  to 

diffused  reflection,  but  quite  opaque, 
due  to  refraction  and  internal  reflec- 
tion. Pour  some  water  into  the  tube, 
and  it  becomes  somewhat  translucent. 
Substitute  spirits  of  turpentine  for 
the  water,  and  the  translucency  is 
increased.  By  mixing  a  small  quantity 
of  carbon  bisulphide  with  the  turpen- 
tine, or  olive  oil  with  oil  of  cassia, 
a  liquid  can  be  obtained  whose  re- 
fractive index  is  about  the  same  as 
that  of  glass,  when  the  light  will 
pass  through  the  liquid  without .  ob- 
struction, and  the  beads  become  trans- 
parent and  nearly  invisible.  The  last 
illustration  shows  that  one  transparent  body  within  another  can  be  -seen 
only  when  their  refractive  powers  differ.  Place  your  eye  on  a  level  with 
the  surface  of  a  hot  stove,  and  you  may  observe  a  wavy  motion  in  the 
air,  due  to  the  mingling  of  currents  of  heated  and  less  refractive  air, 
with  cooler  and  more  refractive  air. 

A  ray  of  light  from  a  heavenly  body  A  (Fig.  261)  undergoes  a 
series  of  refractions  as  it  reaches  successive  strata  of  the  atmos- 
phere of  constantly  increasing  density,  and  to  an  eye  at  the  earth's 
surface  appears  to  come  from  a  point  A'  in  the  heavens.  The  general 
effect  of  the  atmosphere  on  the  path  of  light  that  traverses  it  is  such 
as  to  increase  the  apparent  altitude  of  the  heavenly  bodies.  It  enables 
us  to  see  a  body  (B)  which  is  actually  below  the  horizon,  and  prolongs 
the  apparent  stay  of  the  sun,  moon,  and  other  heavenly  bodies  above 
the  horizon.  Twilight  is  due  both  to  refraction  and  reflection  of  light 
by  the  atmosphere. 


LENSES.  357 

LV.     PRISMS  AND  LENSES. 

§326.  Optical  prisms. —An  optical  prism  is  usually  a 
transparent  wedge-shaped  body.  Figure  262  represents  a 
transverse  section  of  such  a  Fig.  262 

prism.  Let  AB  be  a  ray  of 
light  incident  upon  one  of  its 
surfaces.  On  entering  the 
prism  it  is  refracted  toward  the 
normal,  and  takes  the  direction 
BC.  On  emerging  from  the 
prism,  it  is  again  refracted,  but 
now  from  the  normal  in  the  direction  C  D.  The  object  that 
emits  the  ray  will  appear  to  be  at  F.  Observe  that  the  ray  AB, 
at  both  refractions,  is  bent  toward  the  thicker  part,  or  base,  of 
the  prism. 

§  327.  Lenses.  —  Any  transparent  medium  bounded  by  two 
curved  surfaces,  or  one  plane  and  the  other  curved,  is  a  lens. 

Experiment  1.  Procure  a  couple  of  lenses  thicker  in  the  middle 
than  at  the  edge ;  strong  spectacle  glasses,  or  the  large  lenses  in  an 
opera  glass,  will  answer.  Hold  one  of  the  lenses  in  the  sun's  rays,  and 
notice  the  path  of  the  beam  in  dusty  air  (made  so  by  striking  together 
two  blackboard  rubbers)  after  it  passes  through  the  lens ;  also,  that  on 
a  paper  screen  all  the  rays  may  be  brought  to  a  small  circle,  or  even  a 
point,  not  far  from  ™  263 

the  lens.  This  point 
is  called  the  focus, 
and  its  distance  from 
the  lens,  the  focal 
length  of  the  lens. 

Find     the    focal 

length  of  this  lens,  and  of  the  second,  and  then  of  the  two  together. 
You  find  the  focal  length  of  the  two  combined  is  less  than  of  either 
alone,  and  learn  that  the  more  powerful  a  lens  or  combination  of 
them  is,  the  shorter  the  focal  length ;  that  is,  the  more  quickly  are  the 
parallel  rays  that  enter  different  parts  of  the  lens  brought  to  cross  one 
another. 


358  RADIANT    ENEKGY.  —  LIGHT. 

Experiment  2.  Procure  a  lens  thinner  in  the  middle  than  at  its 
edge.  One  of  the  small  lenses  or  eye-glasses  of  an  opera  glass  will 
answer.  Repeat  the  above  experiment  with  this  lens,  and  notice  that 
the  light  emerging  from  the  lens,  instead  of  coming  to  a  point,  becomes 
spread  out. 

Lenses  are  of  two  classes,  converging  and  diverging,  accord- 
ing as  they  collect  or  scatter  beams  of  light.  Each  class  com- 
prises three  kinds  (Fig.  263)  :  — 

CLASS  I.  CLASS  H. 


1.  Double-convex    "»  Converging  or  convex 

2.  Plano-convex        1      lenses,    thicker     in 

3.  Concavo-convex  [     the  middle  than  at 

(or  meniscus)    J     the  edges. 


,  ( Diverging,    or     con 

4  Double-concave 


I     cave  lenses,  thinner 


5.  Plano-concave       4 

in  the  middle  tnan 


6.  Convexo-concave 


I     at  the  edges. 


A  straight  line,  as  AB,  normal  to  both  surfaces  of  a  lens, 
and  passing  through  its  center  of  curvature,  is  called  its  princi- 
pal axis.  In  every  lens  there  is  a  point  in  the  principal  axis 
called  the  optical  center.  Every  ray  of  light  that  passes  through 
it  has  parallel  directions  at  incidence  and  emergence,  i.e.,  can 
suffer  at  most  only  a  slight  lateral  displacement.  In  lenses  1 
and  4  it  is  half-way  between  their  respective  curved  surfaces. 
A  ray,  drawn  through  the  optical  center  from  any  point  of  an 
object,  as  A  a  (Fig.  269,  p.  362),  is  called  the  secondary  axis 
of  this  point. 

§  328.  Effect  of  lenses. — We  may,  for  convenience  of  illus- 
tration,  regard  a  convex  lens  as  composed, 
approximately,  of  two  prisms  placed  base  to 
base,  as  A  (Fig.  264),  and  a  concave  lens 
as  composed  of  two  prisms  with  their  edges 
in  contact,  as  B.  Inasmuch  as  a  beam  or 
pencil  of  light  ordinarily  strikes  a  lens  in 
such  a  manner  that  the  rays  will  be  bent 
toward  the  thicker  parts  or  bases  of  these 
approximate  prisms,  it  is  obvious  that  the  lens  A  would  tend 
to  bend  the  transmitted  rays  toward  one  another,  while  the 
lens  B  would  tend  to  separate  them.  The  general  effect  of  all 


EFFECT  OF  LENSES. 


359 


convex  lenses  is  to  converge  transmitted  rays;  and  of  concave 
lenses,  to  cause  them  to  diverge.  Incident  rays  parallel  with  the 
principal  axis  of  a  convex  lens  are  brought  to  a  focus  F  (Fig.  265) 
at  a  point  in  the  principal  axis.  This  point  is  called  the  prin- 
cipal focus,  i.e.,  it  is  the  focus  of  incident  rays  parallel  with  the 
principal  axis.  It  may  Fig.  265. 

be  found  by  holding  the 
lens  so  that  the  rays  of 
the  sun  may  fall  perpen- 
dicularly upon  it,  and  then 
moving  a  sheet  of  paper 
back  and  forth  behind  it 
until  the  image  of  the 
sun  formed  on  the  paper  is  brightest  and  smallest.  Or  in  a  room 
it  may  be  found  approximately  by  holding  a  lens  at  a  considerable 
distance  from  a  window,  and  regulating  the  distance  of  the  paper 
so  that  a  distinct  image  of  the  window  will  be  projected  upon  it. 
The  focal  length  is  the  distance  of  the  optical  center  of  the  lens 
to  the  center  of  the  image  on  the  paper.  The  shorter  this 
distance  the  greater  is  the  power  of  the  lens. 

If  the  paper  is  kept  at  the  principal  focus  for  a  short 
time  it  will  take 
fire.  Hence,  this 
is  the  focus  of 
heat  as  well  as  of 
Ught.  The  reason 
is  apparent  why 
convex  lenses  are 
sometimes  called 
" burning  glasses." 
A  pencil  of  rays 
emitted  from  the  principal  focus  F  (Fig.  265),  as  a  luminous 
point,  becomes  parallel  on  emerging  from  a  convex  lens.  If 
the  rays  emanate  from  a  point  nearer  the  lens,  they  diverge  after 
egress,  but  the  divergence  is  less  than  before ;  if  from  a  point 


Fig.  266. 


360  RADIANT    ENERGY. —  LIGHT. 

beyond  the  principal  focus,  the  rays  are  rendered  convergent. 
A  concave  lens  causes  parallel  incident  rays  to  diverge  as  if 
they  came  from  a  point,  as  F  (Fig.  266).  This  point  is  there- 
fore its  principal  focus.  It  is,  of  course,  a  virtual  focus. 

lib* 

§  329.   Conjugate  foci.  —  When  a  luminous  point  S  (Fig. 
Fig.  267.  267)    sends 

rays  to  a  con- 
vex lens,  the 
emergent  rays 
converge  to 
another  point 
S' ;  rays  scut 
from  S'  to  the 

Lens  would  converge  to  S.  Two  points  thus  related  are  called 
conjugate  foci.  The  fact,  that  rays  which  emanate  from  one 
point  are  caused  by  convex  lenses  to  collect  at  one  point, 
gives  rise  to  real  images,  as  in  the  case  of  concave  mirrors. 

§  330.  Images  formed.  —  Fairly  distinct  images  of  objects 
may  be  formed  through  very  small  apertures  (page  330)  ;  but 
owing  to  the  small  amount  of  light  that  passes  through  the 
aperture,  the  images  are  very  deficient  in  brilliancy.  If  the 
aperture  is  enlarged,  brilliancy  is  increased  at  the  expense  of 
distinctness.  (Why?)  A  convex  lens  enables  us  to  obtain  both 
brilliancy  and  distinctness  at  the  same  time. 

Experiment  1.  By  means  of  &porte  lumiere  A  (Fig.  2G8)  introduce  a 
horizontal  beam  of  light  into  a  darkened  room.  In  its  path  place  some 
object,  as  B,  painted  in  transparent  colors  or  photographed  on  glass. 
(Transparent  pictures  are  cheaply  prepared  by  photographers  for  sunlight 
and  lime-light  projections.)  Beyond  the  object  place  a  convex  lens  L, 
and  beyond  the  lens  a  screen  S.  The  object  being  illuminated  by  the 
beam  of  light,  all  the  rays  diverging  from  any  point  a  are  bent  by  the 
lens  so  as  to  come  together  at  the  point  af.  In  like  manner,  all  the  rays 
proceeding  from  c  are  brought  to  the  same  point  d ;  and  so  also  for  all 
intermediate  points.  Thus,  out  of  the  billions  of  rays  emanating  from 


IMAGES   FORMED.  361 

each  of  the  millions  of  points  on  the  object,  those  that  reach  the  lens 
are  guided  by  it,  each  to  its  own  appropriate  point  in  the  image.  It 
is  evident  that  there  must  result  an  image,  both  bright  and  distinct, 
provided  the  screen  is  suitably  placed,  i.e.,  at  the  place  where  the 
rays  meet.  But  if  the  screen  is  placed  at  S'  or  S",  it  is  evident 
that  a  blurred  image  will  be  formed.  Instead  of  moving  the  screen 
back  and  forth,  in  order  to  "focus"  the  rays  properly,  it  is  cus- 
tomary to  move  the  lens. 

Experiment  2.  Fill  some  globular-shaped  glass  vessel  (e.g.,  a  flask, 
decanter,  or  fish-aquarium)  with  water,  and  place  it  lm  in  front  of  a 
white  wall  of  a  darkened  room.  A  little  beyond  the  vessel  place  a 
candle  flame,  and  move  it  back  and  forth  till  a  distinct  image  of  the 
flame  is  projected  upon  the  wall  by  the  water  lens.  Move  the  vessel 
farther  from  the  wall,  and,  on  again  focusing  the  flame,  its  image  will 
be  larger  than  before.  Repeat  the  same  with  a  glass  lens. 

Fig.  268. 


By  properly  varying  the  distances  of  the  lens  and  flame  from 
the  wall,  in  the  last  experiment,  you  may  learn  that  when  the 
distance  of  the  object  is  twice  that  of  the  principal  focus,  the 
object  and  image  are  of  equal  size.  When  the  image  is  within 
twice  the  focal  distance  it  is  less,  and  when  beyond  this  same 
distance  it  is  greater,  than  the  object.  In  all  cases  the  corre- 
sponding linear  dimensions  of  an  object  and  its  image  are  to  one 
another  directly  as  their  respective  distances  from  the  optical  center. 

§  331.  To  construct  the  image  formed  by  a  convex  lens. 
—  Given  the  lens  L  (Fig.  269),  whose  principal  focus  is  at  F  (or  F;, 


362 


RADIANT    ENERGY.  —  LIGHT. 


for  rays  coming  from  the  other  direction),  and  object  AB  in  front  of 
it ;  any  two  of  the  many  rays  from  A  will  determine  where  its  image  a 
is  formed.  The  only  two  that  can  be  traced  easily  are,  the  one  along 
the  secondary  axis  AOa,  and  the  one  parallel  to  the  principal  axis  A  A' ; 


Fig.  289. 


the  latter  will  be  deviated  so  as  to  pass  through  the  principal  focus  F, 
and  will  afterward  intersect  the  principal  axis  at  some  point  a ;  so  this 
is  the  conjugate  focus  of  A;  similarly  for  B,  and  all  intermediate 
points  along  the  arrow.  Thus,  a  real,  inverted  image  is  formed  at  ab. 

Fig.  270. 


§  332.  Virtual  images.  —  Since  rays  that  emanate  from  a 
point  nearer  the  lens  than  the  principal  focus  diverge  after 
egress,  it  is  evident  that  their  focus  must  be  virtual  and  on  the 
same  side  of  the  lens  as  the  object.  Hence,  the  image  of  an 


SPHERICAL  ABERRATION. 


object  placed  nearer  the  lens  than  the  principal  focus  is  virtual, 
magnified,  and  erect,  as  shown  in  Figure  270.  A  convex  lens 
used  in  this  manner  is  called  a  simple  microscope. 

Since  the  effect  of  concave  lenses  is  to  scatter  transmitted 
rays,  pencils  of  rays  emitted  from  A  and  B  (Fig.  271),  after 


Fig.  271. 


refraction,  diverge  as  if  they  came  from  A'  and  B',  and  the 
image  will  appear  to  be  at  A'Bf.  Hence,  images  formed  by 
concave  lenses  are  virtual,  erect,  and  smaller  than  the  object. 

§  333.  Spherical  aberration.  —  In  all  ordinary  convex 
lenses  the  curved  surfaces  are  spherical,  and  the  angles  which 
incident  rays  make  with  the  little  plane  surfaces,  of  which  we 
may  imagine  the  spherical  surface  to  be  made  up,  increase 


Fig.  272. 


rapidly  toward  the  edge  of  the  lens.  Hence,  while  those  rays 
from  a  given  point  of  an  object,  as  A  (Fig.  272),  which  pass 
through  the  central  portion,  meet  approximately  at  the  same 
point  F,  those  which  pass  through  the  marginal  portion  are 
deviated  so  much  that  they  cross  the  axis  at  nearer  points,  e.g.. 


364 


RADIANT    ENERGY.  —  LIGHT. 


at  F' ;  so  a  blurred  image  results.  This  wandering  of  the  rays 
from  a  single  focus  is  called  spherical  aberration.  The  evil  may 
be  largely  corrected  by  interposing  a  diaphragm  DD'  (Fig. 
272) ,  provided  with  a  central  aperture,  smaller  than  the  lens,  so 
as  to  obstruct  those  ra}*s  that  pass  through  the  marginal  part  of 
the  lens. 


Fig.  273. 


LVI.     PRISMATIC   ANALYSIS    OF  LIGHT.  —  SPECTRA. 

§334.  Analysis  of  white  light.  — Experiment  1.  Paste  tin- 
foil smoothly  over  one  side  of  a  glass  plate  about  5cm  square.  In  the 
center  of  the  foil  cut  a  slit  3cm  long  by  lmm  wide,  leaving  smooth 
and  parallel  edges.  Place  the  plate  with  the  slit  in  the  aperture  of 
zporte  lumiere  so  as  to  exclude  all  light  from  a  darkened  room  except 
that  which  passess  through  the  slit.  Near  the  slit  interpose  a  double 
convex  lens  of  (say)  10-inch  focus.  A  narrow  sheet  of  light  will 
traverse  the  room  and  produce  an  image  AB  of  the  slit  on  a  white 
screen  placed  in  its  path.  Now  place  a  glass  prism  C  in  the  path  of 


ANALYSIS   OF  WHITE  LIGHT.  365 

the  beam  with  its  axis  (the  straight  line  connecting  the  centers  of  the 
triangular  faces)  vertical.  (1)  The  light  now  is  not  only  turned  from 
its  former  path,  but  that  which  before  was  a  narrow  sheet,  is,  after 
emerging  from  the  prism,  spread  out  fan-like  into  a  wedge-shaped 
body,  with  its  thickest  part  resting  on  the  screen.  (2)  The  image, 
before  only  a  narrow  vertical  band,  is  now  drawn  out  into  a  long 
horizontal  ribbon  of  light  DE.  (3)  The  image,  before  white,  now 
contains  all  the  colors  of  the  rainbow,  from  red  at  one  end  to  violet 
at  the  other;  it  passes  gradually  through  all  the  gradations  of  orange, 
yellow,  green,  blue,  and  violet.  (The  difference  in  deviation  between 
the  red  and  the  violet  is  purposely  much  exaggerated  in  the  figure.) 

From  this  experiment  we  learn  (1)  that  white  light  is  not  sim- 
ple in  its  composition,  but  the  result  of  a  mixture.  (2)  The  colors 
of  which  white  light  is  composed  may  be  separated  by  refraction. 
(3)  The  cause  of  the  separation  is  due  to  the  different  degrees 
of  deviation  which  they  undergo  by  refraction.  Red,  which  is 
always  least  turned  aside  from  a  straight  path,  is  the  least 
refrangible  color.  Then  follow  orange,  yellow,  green,  blue,  and 
violet  in  the  order  of  their  refrangibility.  The  many-colored 
ribbon  of  light  DE  is  called  the  solar  spectrum.  This  separa- 
tion of  white  light  into  its  constituents  is  called  dispersion.  The 
number  of  colors  of  which  white  light  is  composed  is  really 
infinite,  but  we  have  names  for  only  seven  of  them  ;  viz.,  red, 
orange,  yellow,  green,  cyan-blue,1  ultramarine-blue,  and  violet; 
and  these  are  called  the  primary  or  prismatic  colors.  The 
names  of  the  blues  are  derived  from  the  names  of  the  pigments 
which  most  closely  resemble  them.  The  rainbow  is  an  illustra- 
tion of  a  solar  spectrum  on  a  grand  scale.  It  is  the  result  of 
the  dispersion  of  sunlight  by  rain  drops. 

The  spectrum  may  be  projected  upon  a  screen,  or  it  may  be 
received  directly  by  the  eye,  as  in  the  two  following  experi- 
ments :  — 

Experiment  2.  Upon  a  black  card-board  A  (Fig.  274)  paste  a 
strip  of  white  paper  3cm  long  and  2mm  wide ;  and  place  the  prism  and 
the  eye  as  in  the  figure.  Now  a  beam  of  white  light  from  the  strip  is 

1  See  Rood's  Modern  Chromatics. 


366 


RADIANT    ENERGY.  —  LIGHT. 


Fig.  275. 


refracted  and  dispersed  by  the  prism,  and,  falling  upon  the  retina  of 
the  eye,  you  see,  not  the  narrow  white  strip  in  its  true  position,  but 
a  spectrum  in  the  position  A'.  This  experiment  is  performed  in  a 
lighted  room. 

Experiment  3.  Instead  of  a  continuous  white  strip,  paste  short 
strips  of  red,  white,  and  blue,  end  to  end,  on  the  black  card,  as  repre- 
sented in  Figure  275.  The  spectrum  of  each  color 
is  given  on  the  right,  the  light  portions  repre- 
senting the  illuminated  parts. 
It  will  be  seen  that  in  the 
spectrum  of  the  red,  the  green, 
blue,  and  violet  portions  arc 
almost  completely  dark,  but 
there  is  a  faint  trace  of  or- 
ange ;  in  the  spectrum  of  the 
blue,  the  red,  orange,  and  yel- 
low are  wanting,  blue  and  vio- 
let are  present,  and  a  small 
quantity  of  green.  (What 
lessons  does  this  experiment  teach?) 

Experiment  4.  In  place  of  the  white  strip  of 
paper  used  in  Exp.  2,  admit  light  into  a  dark 
room  through  a  narrow  slit,  and  examine  its  spectrum. 

§  335.  Synthesis  of  white  light.  —  The  composition  of 
white  light  has  been  ascertained  by  the  process  of  analysis  ;  can 
it  be  verified  by  synthesis?  —  i.e.,  can  the  colors  after  dispersion 
be  reunited?  and,  if  so,  will  the  result  of  the  reunion  be  white 
light? 

Experiment  1.  Place  a  second  prism  (2)  in  such  a  position  fi&  that 
light  which  has  passed  through  one  prism  (1),  and  been  refracted  and 
decomposed,  may  be  refracted  back,  and  the  colors  will  be  reblended, 
and  a  white  image  of  the  slit  will  be  restored  on  the  screen. 

Experiment  2.  Place  a  large  convex  lens,  or  a  concave  mirror,  so 
as  to  receive  the  colors  after  dispersion  by  a  prism,  and  bring  the  rays 
to  a  focus  on  a  screen.  The  image  produced  will  be  white. 

Experiment  3.  Receive  the  spectrum  on  a  common  plane  mirror, 
and  rapidly  tip  the  mirror  back  and  forth  in  small  arcs  at  right  angles 
to  the  path  of  the  light,  and  the  light  reflected  by  the  mirror  upon  a 
screen  will  produce  a  white  image  on  the  screen. 


CAUSE   OF   COLOR   AND  DISPERSION.  367 

§  336.  Cause  of  color  and  dispersion.  —  The  color  of  light 
is  determined  solely  by  the  number  of  waves  emitted  by  a  lumi- 
nous body  in  a  second  of  time,  or  by  the  corresponding  wave-length. 
In  a  dense  medium,  the  short  waves  are  more  retarded  than  the 
longer  ones;  hence  they  are  more  refracted.  This  is  the  cause 
of  dispersion.  The  ether  waves  diminish  in  length  from  the 
red  to  the  violet.  As  pitch  depends  on  the  number  of  aerial 
waves  which  strike  the  ear  in  a  second,  so  color  depends  on  the 
number  of  ethereal  waves  which  strike  the  eye  in  a  second. 
From  well-established  data,  determined  by  a  variety  of  methods 
(see  larger  works),  physicists  have  calculated  the  number  of 
waves  that  succeed  one  another  for  each  of  the  several  prismatic 
colors,  and  the  corresponding  wave-lengths  ;  the  following  table 
contains  the  results.  The  letters  A,  C,  D,  etc.,  refer  to  Fraun- 
hofer's  lines  (see  page  370). 

Length  of  waves  No.  of  waves 

in  millimeters.  per  second. 

Dark  red A 000760 395,000,000,000,000 

Orange C 000656 458,000,000,000,000 

Yellow D 000569 510,000,000,000,000 

Green E 000527 570,000,000,000,000 

C.  Blue F 000486 618,000,000,000,000 

U.  Blue G 000431 697,000,000,000,000 

Violet H 000397 760,000,000,000,000 

There  is  a  limit  to  the  sensibility  of  the  eye  as  well  as  of  the 
ear.  The  limit  in  the  number  of  vibrations  appreciable  by  the 
eye  lies  approximately  within  the  range  of  numbers  given  in  the 
above  table  ;  i.e.,  if  the  succession  of  waves  is  much  more  or  less 
rapid  than  indicated  by  these  numbers,  they  do  not  produce  the 
sensation  of  sight.  It  is  evident  that  the  frequency  of  the  waves 
emitted  by  a  luminous  body,  and  consequently  the  color  of  the 
light  emitted,  must  depend  on  the  rapidity  of  the  vibratory  mo- 
tions of  the  molecules  of  that  body,  i.e.,  upon  its  temperature. 
This  has  been  shown  in  a  convincing  manner  as  follows :  The 
temperature  of  a  platinum  wire  is  slowly  raised  by  passing  a 
gradually  increasing  current  of  electricity  through  it.  At  a 


368  RADIANT    ENERGY.  —  LIGHT. 

f 

temperature  of  about  540°  C.  it  begins  to  emit  light ;  and  the 
light,  analyzed  by  a  prism,  shows  that  it  emits  only  red  light. 
As  the  temperature  rises,  there  will  be  added  to  the  red  of  the 
spectrum,  first  yellow,  then  green,  blue,  and  violet  successively. 
When  it  reaches  a  white  heat,  it  emits  all  the  prismatic  colors. 
It  is  significant  that  a  white-hot  body  emits  more  red  light  than 
a  red-hot  body,  and  likewise  more  light  of  every  color  than  at 
any  lower  temperature.  The  conclusion  is,  that  a  body  which 
emits  white  light  sends  forth  simultaneously  waves  of  a  variety  of 
lengths. 

§  337.  Continuous  spectra.  —  The  spectrum  produced  by 
the  platinum  is  continuous ;  that  is,  the  band  of  light  is  un- 
broken. If  the  spectrum  is  not  complete,  as  when  the  tempera- 
ture is  too  low,  it  will  begin  with  red,  and  be  continuous  as  far 
as  it  goes.  All  luminous  solids  and  liquids  give  continuous 
spectra. 


Fig.  276. 


§  338.  Spectroscope.  —  A  small  instrument  called  a  pocket 
spectroscope1  will  answer  for  all  experiments  given  in  this  book.  More 
elaborate  experiments  require  more  elaborate  apparatus,  a  description 
of  which  must  be  sought  for  in  larger  works  on  this  subject.  This 
instrument  contains  three  or  more  prisms,  A,  B,  and  C  (Fig.  276).  The 
prisms  are  enclosed  in  a  brass  tube  D,  and  this  tube  in  another  tube  E. 
F  is  a  convex  lens,  and  G  is  an  adjustable  slit.  By  moving  the  inner 
tube  back  and  forth,  the  instrument  may  be  so  focused  that  parallel 
.rays  will  fall  upon  prism  A.  By  varying  the  kind  of  glass  used  in  the 
different  prisms,8  as  well  as  their  structure,  the  deviation  of  light  from 
a  straight  path,  in  passing  through  them,  is  overcome,  while  the  dis- 
persion is  preserved.  On  account  of  the  directness  of  the  path  of  light 
through  it,  this  instrument  is  called  a  direct-vision  spectroscope. 

'    J  It  is  expected  that  the  pupil  will  be  provided  with  a  pocket  spectroscope,  the  cost  of 
which  neerl  not  exceed  ten  dollars. 

"•  A  and  C  are  crown-glass,  and  B  is  flint-glass.    Sec  foot-note,  p.  395. 


BRIGHT-LINE   SPECTRA.  369 

§  339.   Bright  line,  absorption,  or  re  versed,  spectra. — 

Experiment  1.  Open  the  slit  a  little  less  than  lmm  wide,  and  look 
through  the  spectroscope  at  the  sky  (not  at  the  sun,  for  its  light  is  too 
intense  for  the  eye) ,  and  you  will  see  a  continuous  spectrum. 

Experiment  2.  Repeat  the  last  experiment  with  a  candle,  kerosene, 
or  ordinary  gas  flame,  and  you  will  obtain  similar  results. 

Experiment  3.  Take  a  piece  of  platinum  wire  10cm  long,  seal  one 
end  of  it  by  fusion  to  a  short  glass  tube  for  a  handle,  and  make  a  loop  at 
the  other  end  about  lmm  in  diameter.  Wet  the  loop  in  clean  water, 
dip  it  into  pulverized  common  salt,  and  introduce  it  into  the  almost  in- 
visible and  colorless  flame  of  a  Bunsen  burner.  Instantly  the  flame 
becomes  luminous  and  colored  a  deep  yellow.  Examine  the  light  with  a 
spectroscope,  and  you  will  find,  instead  of  a  continuous  spectrum  be- 
ginning with  red,  only  a  bright,  narrow  line  of  yellow  in  the  yellow  part 
of  the  spectrum,  next  the  orange.  Your  spectrum  consists  essentially 
of  a  single  bright  yellow  line  on  a  comparatively  dark  ground  (see 
Sodium,  Mg.  277). 

Experiment  4.  Heat  the  platinum  loop  until  it  ceases  to  color  the 
flame,  then  wet  it  and  dip  it  into  chloride  of  lithium,  and  repeat  the 
last  experiment.  You  obtain  a  carmine-tinted  flame,  and  see  through 
the  spectroscope  a  bright  red  line  and  a  faint  orange  line  (see  Lithium, 
Fig.  277). 

Experiment  5.  Use  potassium  hydrate,  and  you  obtain  a  violet- 
colored  flame,  and  a  spectrum  consisting  of  a  red  line  and  a  violet  line 
(the  latter  quickly  disappears).  Use  strontium  nitrate,  and  obtain  a 
crimson  flame,  and  a  spectrum  consisting  of  several  lines  in  the  red 
and  the  orange,  and  a  blue  line.  (See  Potass,  and  Stron.,  Tig.  277.) 
.  .  Experiment  6.  Use  a  mixture  of  several  of  the  above  chemicals, 
and.  you  will  obtain  a  spectrum  containing  all  the  lines  that  characterize 
the  several  substances. 

Every  chemical  compound  used  in  the  above  experiments 
contains  a  different  metal,  e.g.,  common  salt  contains  the  metal 
sodium  ;  the  other-  substances  used  successively  contain  respec- 
tively the  metals  lithium,  potassium.,  and  strontium.  These 
metals,  when  introduced  into  the  flame,  are  vaporized,  and  we 
get their  spectra  when  in  a  gaseous  state.  All  gases  give  dis- 
continuous, or  bright  line,  spectra,  and  no  two  gases  give  the  same 
spectra.  -The  fact  that  in  the  second  experiment  we  obtained 
continuous  and  similar  spectra,  appears  to  contradict  the  last 


370 


RADIANT    ENERGY.  —  LIGHT. 


two  statements.  But  it  should  be  remembered  that  all  that 
gives  light  in  those  flames  is  small  particles  of  solid  carbon 
floating  in  the  burning  gas.  We  see,  then,  that  the  spectroscope 
furnishes  us  with  a  reliable  means  of  determining,  at  any  time, 
whether  light  proceeds  from  a  luminous  solid  or  a  luminous  gas. 


R, 


O.       Y. 


Fig.  277. 
G.  C.B.        U.B. 


V. 


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.hill  I.I. 

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50               70               90              110             130             150             1 

1    I    i  1  !  1  1    i    1  1  i    1    il  II  ll  1    1  1  1      1  1    lllllll    !    I        1 

ABCD            EbF                        G                     HH' 

1 

§  340.  Dark-line  spectra.  —  Experiment  1.  Close  the  slit  of 
the  spectroscope  so  that  the  aperture  will  be  very  narrow ;  direct  it 
once  more  to  the  sky,  and  slowly  move  the  inner  tube  back  and  forth, 
and  you  will  find,  with  a  certain  suitable  adjustment  which  may  be 
obtained  by  patient  trial,  that  the  solar  spectrum  is  not  in  reality  con- 
tinuous, but  is  crossed  by  several  dark  lines  (see  Fig.  277). 

Experiment  2.  The  electric  light  is  now  in  so  common  use  that  it 
may  be  possible  to  perform  this  experiment.  Between  the  electric 
light  and  the  spectroscope  introduce  the  flame  of  a  Bunsen  burner,  and 
color  it  yellow  with  salt.  Examine  the  electric  light  transmitted 
through  this  yellow  flame. 

In  the  last  experiment  you  will  naturally  expect  to  find  the 
yellow  part  of  the  spectrum  uncommonly  bright,  for  there  would 


SPECTRUM   ANALYSIS.  371 

apparently  be  added  to  the  }'ellow  of  the  electric  light  the  yellow 
of  the  salted  flame.  But  precisely  where  }'ou  would  look  for  the 
brightest  yellow,  there  you  discover  that  the  spectrum  is  crossed 
by  a  dark  line.  If  you  use  salts  of  lithium,  potassium,  and 
strontium  in  a  similar  manner,  }'ou  will  find  in  every  case  your 
spectrum  crossed  by  dark  lines  where  }'ou  would  expect  to  find 
bright  lines.  Remove  the  Bunsen  flame,  and  the  dark  lines 
disappear.  It  thus  appears  that  the  vapors  of  different  sub- 
stances absorb  or  quench  the  very  same  rays  that  they  are  capable 
of  emitting ;  very  much,  it  would  seem,  as  a  given  tuning-fork 
selects  from  various  sounds  only  those  of  a  definite  wave-length 
corresponding  to  its  own  vibration-period.  The  dark  places  of 
the  spectrum  receive  light  in  full  force  from  the  salted  flame ; 
but  the  light  is  so  feeble,  in  comparison  with  those  places  illumi- 
nated by  the  electric  light,  that  the  former  appear  dark  by  con- 
trast. Light  transmitted  through  certain  liquids  (as  sulphate  of 
quinine  and  blood)  and  certain  solids  (as  some  colored  glasses) 
produces  dark-line  spectra.  These  spectra  are  obtained  only 
when  light  passes  through  media  capable  of  absorbing  rays  of 
certain  wave-length ;  hence,  they  are  commonly  called  absorp- 
tion spectra.  Since  a  given  vapor  causes  dark  lines  precisely 
where,  if  it  were  itself  the  only  radiator  of  light,  it  would  cause 
bright  lines,  dark-line  spectra  are  frequently  called  reversed 
spectra.  There  are  then  three  kinds  of  spectra :  continuous 
spectra,  produced  by  luminous  solids,  liquids,  or,  as  has  been 
found  in  a  few  instances,  gases  under  great  pressure ;  bright- 
line  spectra,  produced  by  luminous  vapors  ;  and  absorption  spec- 
tra, produced  by  light  that  has  been  sifted  by  certain  media. 

§  341.  Spectrum  analysis.  — More  elaborate  spectroscopes 
contain  many  prisms,  by  which  we  greatly  increase  the  purity  of 
the  spectrum.  (By  purity  is  meant  a  freedom  from  the  over- 
lapping of  images  of  the  slit,  by  which  many  lines  of  the 
spectra  are  concealed.)  They  also  contain  an  illuminated  scale 
which  may  be  seen  adjacent  to  the  spectrum,  by  which  the  exact 


RADIANT    ENERGY.  —  LIGHT. 

position  of  the  lines,  and  their  relative  distances  from  one  another, 
can  be  accurately  determined,  and  a  telescope  by  which  the  spec- 
trum and  scale  may  be  magnified.  The  positions  of  some  of  the 
prominent  lines  of  the  solar  spectrum  were  first  determined, 
mapped,  and  distinguished  from  one  another  by  certain  letters 
of  the  alphabet  by  Fraunhofer ;  hence,  the  dark  lines  of  the 
solar  spectrum  are  commonly  called  Fraunhofer's  lines.  So 
far  as  discovered,  no  two  substances  have  a  spectrum  con- 
sisting of  the  same  combination  of  lines ;  and,  in  general, 
different  substances  but  very  rarely  possess  lines  appearing  to 
be  common  to  both.  Hence,  when  we  have  once  observed  and 
mapped  the  spectrum  of  any  substance,  we  may  ever  after  be 
able  to  recognize  the  presence  of  that  substance,  when  emit- 
ting light,  whether  it  is  in  our  laboratory  or  in  a  distant 
heavenly  body.  The  spectroscope,  therefore,  furnishes  us  a 
most  efficient  means  of  detecting  the  presence  (or  absence)  of 
any  elementary  substance,  even  when  it  is  combined  or  mixed 
with  other  substances.  It  is  not  necessary  that  the  given  sub- 
stance should  exist  in  large  quantities  ;  for  example,  the  four- 
teen-millionth part  of  a  milligram  of  sodium  can  be  detected  by 
the  spectroscope.  Substances  that  are  not  easily  converted  into 
vapors  at  low  temperatures  may  be  placed  between  the  poles 
of  an  electric  battery  or  an  induction  coil.  The  heat  generated 
by  electricity  will  vaporize  all  substances.  After  maps  of  the 
spectra  of  all  known  substances  have  been  made  out,  if,  on  ex- 
amination of  a  complex  substance,  any  new  lines  should  at  any 
time  appear  in  the  spectrum,  it  would  indicate  the  presence  of 
a  substance  hitherto  undiscovered.  It  was  thus  that  the  elements, 
caesium,  rubidium,  thallium,  and  indium  were  discovered. 

§  342.  Celestial  chemistry  and  physics.  —  The  spectrum 
of  iron  has  been  mapped  to  the  extent  of  460  bright  lines.  The 
solar  spectrum  furnishes  dark  lines  corresponding  to  nearly  all 
these  bright  lines.  Can  there  be  any  doubt  of  the  existence  of 
iron  in  the  sun  ?  By  examination  of  the  reversed  spectrum  of 


HEAT   AND   CHEMICAL   SPECTRA.  373 

the  sun,  we  are  able  to  determine  with  certainty  the  existence 
there  of  sodium,  calcium,  copper,  zinc,  magnesium,  hydro- 
gen, and  many  other  known  substances.  Again,  from  our 
knowledge  of  the  way  in  which  a  reversed  spectrum  can  be  pro- 
duced, we  may  conclude  that  the  sun  consists  of  a  luminous 
solid,  liquid,  or  an  intensely  heated  and  greatly  condensed  gas 
(called  a  photosphere) ,  and  that  this  nucleus  is  surrounded  by 
an  atmosphere  of  cooler  vapor,  in  which  exist  at  least  all  the 
substances  just  named.  The  moon  and  other  heavenly  bodies 
that  are  visible  only  by  reflected  sun-light  give  the  same  spectra 
as  the  sun,  while  those  that  are  self-luminous  give  spectra  which 
differ  from  the  solar  spectrum. 

§  343.  Heat  and  chemical  spectra.  —  If  a  sensitive  ther- 
mometer is  placed  in  different  parts  of  the  solar  spectrum,  it 
will  indicate  heat  in  all  parts  ;  but  the  heat  generally  increases 
from  the  violet  toward  the  red.  It  does  not  cease,  however,  with 
the  limit  of  the  visible  spectrum ;  indeed,  if  the  prism  is  made 
of  flint  glass,  the  greatest  heat  is  just  beyond  the  red.  A  strip 
of  paper  wet  with  a  solution  of  chloride  of  silver  suffers  no 
change  in  the  dark ;  in  the  light  it  quickly  turns  black ;  ex- 
posed to  the  light  of  the  solar  spectrum,  it  turns  dark,  but 
quite  unevenly.  The  change  is  slowest  in  the  red,  and  con- 
stantly increases,  till  about  the  region  indicated  by  G  (Fig.  277) , 
when  it  attains  its  maximum ;  from  this  point  it  falls  off,  and 
ceases  at  a  point  considerably  beyond  the  limit  of  the  violet. 
It  thus  appears  that  the  solar  spectrum  is  not  limited  to  the 
visible  spectrum,  but  extends  beyond  at  each  extremity.  Those 
rays  that  lie  beyond  the  red  are  usually  called  the  ultra-red 
rays,  while  those  that  lie  beyond  the  violet  are  called  the  ultra- 
violet rays.  The  ultra-red  rays  are  of  longer  vibration-period, 
and  the  ultra-violet  of  shorter  period,  than  the  luminous  rays. 

§  344.  Only  one  kind  of  radiation.  —  The  fact  that  radi- 
ant energy  produces  three  distinct  effects,  —  viz.,  luminous, 
heating,  and  chemical,  —  has  given  rise  to  a  quite  prevalent  idea 


374  RADIANT    ENERGY.  —  LIGHT. 

that  there  are  three  distinct  kinds  of  radiation.  There  is,  how- 
ever, absolutely  no  proof  that  these  different  effects  are  produced 
by  different  kinds  of  radiation.  The  same  radiation  that  produ- 
ces vision  can  generate  heat  and  chemical  action.  The  fact  that 
the  ultra-red  and  ultra-violet  rays  do  not  affect  the  eye  does 
not  argue  that  they  are  of  a  different  nature  from  those  that  do, 
but  it  does  show  that  there  is  a  limit  to  the  susceptibility  of  the 
eye  to  receive  impressions  from  radiation.  Just  as  there  are 
sound-waves  of  too  long,  and  others  of  too  short,  period  to 
affect  the  ear,  so  there  are  etherial  waves,  some  of  too  long,  and 
others  of  too  short,  period  to  affect  the  eye.  It  is  true,  how- 
ever, that  waves  of  long  period  from  the  sun  are  more  energetic 
in  producing  heating  effects  than  those  of  short  period ;  and 
those  of  short  period  are  more  effective  in  generating  chemical 
action  in  certain  substances  than  those  of  long  period ;  while 
only  those  which  lie  between  the  extremes  affect  the  eye. 


LVII.    COLOR. 

§  345.  Color  produced  by  absorption.  —  "  All  objects  are 
black  in  the  dark ;  "  this  is  equivalent  to  saying  that  without 
light  there  is  no  color.  Is  color  a  quality  of  an  object,  or  is  it  a 
quality  of  the  light  which  illuminates  the  object? 

Experiment  1.  We  have  found  that  common  salt  introduced  into 
a  Bunsen  flame  renders  it  luminous,  and  that  the  light  when  analyzed 
with  a  prism  is  found  to  contain  only  yellow.  Expose  papers  or 
fabrics  of  various  colors  to  this  light  in  a  darkened  room.  No  one  of 
them  exhibits  its  natural  color  except  yellow. 

Experiment  2.  Hold  a  narrow  strip  of  red  paper  or  ribbon  in  the 
red  portion  of  the  solar  spectrum ;  it  appears  red.  Slowly  move  it 
toward  the  other  end  of  the  spectrum ;  on  leaving  the  red  it  becomes 
darker,  and  when  it  reaches  the  green  it  is  quite  black  or  colorless,  and 
remains  so  as  it  passes  the  other  colors  of  the  spectrum.  Repeat  the 
experiment,  using  other  colors,  and  notice  that  only  in  light  of  its  own 
color  does  each  strip  of  paper  appear  of  its  natural  color ;  while  in  all 
other  colors  it  is  dark. 


SKY  COLORS.  375 

These  experiments  show  that  (1)  color  is  a  quality  of  the  light 
which  illuminates,  and  not  of  the  object  illuminated;  (2)  in  order 
that  an  object  may  appear  of  a  certain  color,  it  must  receive  light 
of  that  color;  and  of  course  if  it  receives  other  colors  at  the  same 
time,  it  must  be  capable  of  absorbing  them.  The  energy  of  the 
waves  absorbed  is  converted  into  heat,  and  warms  the  object. 
When  white  light  strikes  an  object,  it  appears  white  if  it  reflects 
all  the  colors.  If  red  light  falls  upon  the  same  object,  it  appears 
red,  for  it  is  capable  of  reflecting  red ;  or  it  appears  green,  if 
green  light  alone  falls  on  it.  If  white  light  falls  upon  an  object, 
and  all  the  colors  are  absorbed  except  the  blue,  the  object  ap- 
pears blue.  When  we  paint  our  houses  we  do  not  apply  color 
to  them.  We  apply  substances  called  pigments,  that  have  a 
property  of  absorbing  all  the  colors  except  those  which  we  would 
have  our  houses  appear. 

Experiment  3.  By  means  of  a  porte  lumiere  introduce  a  beam  of 
light  into  a  dark  room.  Cover  the  orifice  with  a  deep  red  (copper)  glass. 
The  white  light,  in  passing  through  the  glass,  appears  to  be  colored 
red.  Does  the  glass  color  the  light  red  ? 

Experiment  4.  With  the  slit  and  prism  form  a  solar  spectrum,  and 
between  the  prism  and  screen  interpose  the  red  glass.  All  the  colors 
of  the  spectrum  instantly  disappear  except  the  red. 

It  thus  appears  that  a  red  transparent  bod}r  transmits  only 
red,  and  absorbs  all  other  colors.  No  body  gives  color  to  light 
that  it  reflects  or  transmits. 

§  346.  Sky  colors.  — Experiment  1.  Dissolve  a  little  white  cas- 
tile  soap  in  a  tumbler  of  water ;  or,  better,  stir  into  the  water  a  few  drops 
of  an  alcoholic  solution  of  mastic,  enough  to  render  the  water  slightly 
turbid.  Place  a  black  screen  behind  the  tumbler,  and  examine  the  liquid 
by  reflected  sunlight,  —  the  liquid  appears  to  be  blue;  examine  the 
liquid  by  transmitted  sunshine,  —  it  now  appears  yellowish  red. 

Skylight  is  reflected  light.  The  particles  of  atmospheric  dust 
(of  water,  probably)  that  pervade  the  atmosphere,  like  the  fine 
particles  of  mastic  suspended  in  the  water,  reflect  blue  light ; 
while,  beyond  the  atmosphere,  is  a  black  background  of  darkness. 


376  RADIANT    ENERGY.  —  LIGHT. 

But  we  must  not,  from  this,  conclude  that  the  atmosphere  is 
blue  ;  for,  unlike  blue  glass,  but  like  the  turbid  liquid,  it  trans- 
mits yellow  and  red  ra}rs  freely,  so  that,  seen  by  reflected 
light  it  is  blue,  but  seen  by  transmitted  light  it  is  yellowish  red. 

Experiment  2.  Pour  some  of  the  turbid  liquid  into  a  small  test- 
tube,  and  examine  it  and  the  tumbler  of  liquid  by  transmitted  light ; 
the  former  appears  almost  colorless,  while  the  latter  is  quite  deeply 
colored. 

When  the  sun  is  near  the  horizon,  its  rays  travel  a  greater 
distance  in  the  air  to  reach  the  earth  than  when  it  is  in  the  zenith 
(see  Fig.  261,  p.  356)  ;  consequently,  there  is  a  greater  loss  by 
absorption  and  reflection  in  the  former  case  than  in  the  latter. 
But  the  yellow  and  red  rays  suffer  less  destruction,  proportionally, 
than  the  other  colors ;  consequently,  these  colors  predominate 
in  the  morning  and  evening. 

§  347.  Mixing"  colors.  —  A  mixture  of  all  the  prismatic 
colors,  in  the  proportion  found  in  sunlight,  produces  white. 
Can  white  be  produced  in  any  other  way  ? 

Experiment  1.    On  a  black  surface  A  (Fig.  278),  about  4cm  apart, 
lay  two  small  rectangular  pieces  of  paper,  one  yellow  and  the  other 
blue.  In  a  vertical  position  between,  and  from  4cm  to 
gem  above  these  papers,  hold  a  slip  of  plate  glass  C. 
Looking  obliquely  down  through  the  glass  you  may 
see  the  blue  paper  by  transmitted  light  and  the  yel- 
low paper  by  reflection.     That  is,  you  see  the  object 
itself  in  the  former  case  and  the  image  of  the  object 
in  the  latter  case.     By  a  little  manipulation,  the 
image  and  the  object  may  be  made  to  overlap  one 
another,  when  both  colors  will  apparently  disappear, 
and  in  their  place  the  color  which  is  the  result  of 
the  mixture  will  appear.    In  this  case  it  will  be 
white,  or,  rather,  gray,  which  is  white  of  a  low  de- 
gree  of   luminosity.      If   the  color    is    yellowish, 
lower  the  glass;  if  bluish,  raise  it. 
Experiment  2.  Cut  out  of  stiff  drawing-paper  two  circular  disks, 
each  16cm  in  djameter.    Paint  one  with  chrome  yellow,  and  the  other 
with  ultramarine  blue.     Cut  a  radial  slit  in  each,  and  pass  an  edge  of 


MIXING    COLORS. 


3TT 


one  slit  through  the  slit  of  the  other,  and  so  arrange  them  that  one 
shall  partly  conceal  the  other,  leaving  rather  more  blue  exposed  than  of 
the  yellow,  as  in  Figure  279.  Attach  the  disks  so  combined  to  some 
apparatus  by  which  they  may  be  rapidly  rotated;  for  example,  to  a 
"  color  top,"  such  as  are  sold  £fe  toy  stores.  Rotate  the  disks,  and  the 
colors  will  be  so  blended  in  the  eye  as  to  appear  gray ;  or,  if  either  color 
predominates,  arrange  the  disks  so  that  less  of  that  color  will  be  ex- 
posed. Figure  280  represents  "  Newton's  disk,"  which  contains  the 
seven  prismatic  colors  arranged  in  a  proper  proportion  to  produce  gray 
when  rotated. 


Fig.  279. 


Fig.  280. 


Fig.  281. 


In    a   like    manner,  Fig.  282. 

you  may  produce  white 
by  mixing  purple  and 
green  ;  or,  if  any  color 
on  the  circumference 
of  the  circle  (Fig.  282) 
is  mixed  with  the  color 
exactly  opposite,  the 
resulting  color  will  be 
white.  Again,  the  three 
colors,  red,  green,  and 
violet,  arranged  as  in 
Figure  281,  with  rather 
less  surface  of  the 
green  exposed  than  of 
the  other  colors,  will 

give  gray.  Green  mixed  with  red,  in  varying  proportions,  will 
produce  any  of  the  colors  between  these  two  colors  in  the  dia- 
gram (Fig.  282) ;  green  mixed  with  violet  will  produce  any  of 


378  RADIANT   ENERGY.  —  LIGHT. 

the  colors  between  them  ;  and  violet  mixed  with  red  gives  purple  ; 
but  no  two  colors  mixed  will  produce  any  of  these  three  colors. 
Hence,  a  very  widely  accepted  theory  is  adopted  by  many,  that 
red,  green,  and  violet  are  the  three  primary  color  sensations,  and 
that  the  other  colors  of  the  spectrum  are  simply  the  products  of 
mixtures,  in  varying  proportions,  of  these  three. 

§  348.  Mixing  pigments.  —  Experiment  1.  Mix  a  little  of  the 
two  pigments,  chrome  yellow  and  ultramarine  blue,  and  you  obtain  a 
green  pigment. 

The  last  three  experiments  show  that  mixing  certain  colors, 
and  mixing  pigments  of  the  same  name,  may  produce  very 
different  results.  In  the  first  experiments  you  actually  mixed 
colors  ;  in  the  last  experiment  you  did  not  mix  colors,  and  we 
must  seek  an  explanation  of  the  result  obtained.  If  a  glass 
vessel  with  parallel  sides  containing  a  blue  solution  of  sulphate 
of  copper  is  interposed  in  the  path  of  light  which  forms  a  solar 
spectrum,  it  will  be  found  that  the  red,  orange,  and  yellow  rays 
are  cut  out  of  the  spectrum,  i.e.,  the  liquid  absorbs  these  rays. 
And  if  a  yellow  solution  of  bichromate  of  potash  is  interposed,  the 
blue  and  violet  rays  will  be  absorbed.  It  is  evident  that,  if  both 
solutions  are  interposed,  all  the  colors  will  be  destroyed  except 
the  green,  which  alone  will  be  transmitted  ;  thus  :  — 

Cancelled  by  the  blue  solution,     $  <j)  /  G  B  V. 
Cancelled  by  the  yellow  solution,     R  O  Y  G 
Cancelled  by  both  solutions,  jk  fi  /  G 


In  a  similar  manner,  when  white  light  strikes  a  mixture  of 
yellow  and  blue  pigments  on  the  palette,  it  penetrates  to  some 
depth  into  the  mixture  ;  and,  during  its  passage  in  and  out,  all  the 
colors  are  destroyed  except  the  green  ;  so  the  mixed  pigments 
necessarily  appear  green.  But,  when  a  mixture  of  yellow  and 
blue  lights  enters  the  eye,  we  get,  as  the  result  of  the  combined 
sensations  produced  by  the  two  colors,  the  sensation  of  white  ; 
hence,  a  mixture  of  yellow  and  blue  gives  white. 


EFFECT  OF   CONTRAST.  379 

§  349.  Complementary  colors.  —  Experiment.  On  a  piece  of 
white,  or  better,  gray  paper,  lay  a  circular  piece  of  blue  paper  15mm  in 
diameter.  Attach  one  end  of  a  piece  of  thread  to  the  colored  paper, 
and  hold  the  other  end  in  the  hand.  Place  the  eyes  within  about  15C™ 
of  the  colored  paper,  and  look  steadily  at  the  center  of  the  paper  for 
about  fifteen  seconds ;  then,  without  moving  the  eyes,  suddenly  pull 
the  colored  paper  away,  and  instantly  there  will  appear  on  the  gray 
paper  an  image  of  the  colored  paper,  — but  the  image  will  appear  to  be 
yellow.  This  is  usually  called  an  after-image.  If  yellow  paper  is  used, 
the  color  of  the  after-image  will  be  blue ;  and  if  any  other  color  given  in 
the  diagram,  Figure  282,  the  color  of  its  after-image  will  be  the  color 
that  stands  opposite  to  it. 

This  phenomenon  is  explained  as  follows :  When  we  look 
steadily  at  blue  for  a  time,  the  eyes  become  fatigued  by  this 
color,  and  less  susceptible  to  its  influence,  while  they  are  fully 
susceptible  to  the  influence  of  other  colors  ;  so  that  when  they 
are  suddenly  brought  to  look  at  white,  which  is  a  compound  of 
yellow  and  blue,  they  receive  a  vivid  impression  from  the  for- 
mer, and  a  feeble  impression  from  the  latter ;  hence,  the  pre- 
dominant sensation  is  3*ellow.  Any  two  colors  which  together 
produce  white  are  said  to  be  complementary  to  each  other. 
The  opposite  colors  in  the  diagram,  Figure  282,  are  complement- 
ary to  one  another. 

§  350.  Effect  of  contrast.  —  When  any  two  colors  given  in 
the  circle,  Figure  282,  are  brought  in  contrast,  as  when  they 
are  placed  next  one  another,  the  effect  is  to  move  them  farther 
apart.  For  example,  if  red  and  orange  are 'brought  in  contrast, 
the  orange  assumes  more  of  a  yellowish  hue,  and  the  red  more 
of  a  purplish  hue.  Colors  that  are  already  as  far  apart  as  pos- 
sible, e.g.,  yellow  and  blue,  do  not  change  their  hue,  but  merely 
cause  one  another  to  appear  more  brilliant. 

§  351.   Color  produced  by  interference.  —  Experiment  1. 

In  a  vise  or  other  convenient  instrument,  press  two  clean  pieces  of 
thick  plate  glass  firmly  together.  A  number  of  colors  will  be  seen 
arranged  in  a  certain  order,  and  forming  curves  more  or  less  regular 
around  the  point  of  pressure. 


380  RADIANT    ENERGY.  —  LIGHT. 

Experiment  2.  Paint  one  side  of  a  piece  of  window  glass  with  In- 
dia ink  so  as  to  render  it  quite  opaque ;  then,  when  dry,  with  the  point 
of  a  needle  rule  fifteen  to  twenty  parallel  lines  in  the  ink,  about  2mm 
apart,  cutting  quite  through  the  ink,  so  that  light  may  pass  through  the 
scratches.  Now  stand  at  a  distance  of  ten  feet  or  more  from  a  kerosine 
or  gas  flame,  and  look  through  the  glass  with  one  eye  at  the  flame, 
edge  on ;  move  the  glass  to  and  from  the  eye  slowly,  so  as  to  properly 
focus  it,  and  you  will  see  many  spectra  of  the  flame  on  each  side  of  it, 
separated  by  dark  intervals. 

Experiment  3.  Place  the  ruled  glass  in  the  path  of  a  beam  of  light 
thrown  into  a  dark  room  by  a  porte  lumiere,  and  project  an  image  of  the 
glass  on  a  screen  by  means  of  a  convex  lens  of  two  to  five  inches  focal 
length,  and  you  will  obtain  a  series  of  beautiful  spectra. 

Tig.  283. 


If  in  the  path  of  the  beam  a  red  glass  is  interposed,  a  large 
number  of  alternating  red  and  dark  lines  may  be  obtained,  though 
the  experiment  is  a  difficult  one.  Let  us  study  the  last  result. 
Let  the  series  of  parallel  lines  AB  (Fig.  283)  represent  the 
series  of  waves  constituting  the  beam  of  light  before  it  strikes 
the  ruled  glass  CD ;  and  EF,  the  portions  of  the  same  waves 
that  succeed  in  passing  through  the  scratches,  GH  and  MN. 
The  wave-lengths  and  the  width  of  the  scratches,  etc.,  are 


*  COLOR   PRODUCED   BY  INTERFERENCE.  381 

immensely  exaggerated  in  the  diagram.  Now,  rf  you  watch 
waves  of  water  as  they  beat  against  an  obstacle  rising  above  its 
surface,  you  will  see  that  part  of  their  energy  is  expended  in 
forming  a  new  set  of  waves,  which  we  will  call  secondary  waves, 
radiating  from  the  obstacle  and  winding  around  behind  it.  In  a 
similar  manner,  secondary  waves  of  light  are  generated  at  the 
edges  of  obstacles  against  which  light  grazes.  This  apparent 
bending  of  the  waves  of  light  round  the  edges  of  opaque  bodies 
receives  the  name  of  diffraction.  Sections  of  such  waves  are 
represented  in  the  diagram  as  crossing  the  original  or  primary 
waves  at  certain  points,  and  also  one  another,  behind  the  obsta- 
cle M.  The  continuous  lines  represent  one  phase  of  the  waves, 
and  the  dotted  lines  the  opposite  phase,  as  crest  and  trough. 
Now,  it  will  be  seen  that  at  certain  points  (denoted  by  heavy 
dots)  which  lie  in  the  same  line  as  a 6,  the  primary  and  secondary 
waves  meet  in  similar  phases  ;  and  the  consequence  is,  that  the 
point  b  of  the  screen  O  P  is  illuminated  by  the  combined  action 
of  the  two  sets  of  waves.  But  at  other  points  (denoted  by 
small  crosses) ,  as  cd,  the  opposite  phases  of  the  two  sets  of 
waves  coincide  with  one  another,  and  the  result  is  that  they 
tend  to  neutralize  one  another ;  and  consequently  the  point  d 
of  the  screen  is  deprived  of  light,  and  a  dark  line  occurs  at 
this  place.  In  a  similar  manner  the  points  h,  i,  j,  etc.,  are 
illuminated  by  the  joint  action  of  the  two  sets  of  waves,  while 
the  points  e,  /,  g,  etc.,  are  deprived  of  light  by  their  mutual 
destruction.  Such  will  be  the  result  when  monochromatic  light, 
or  light  of  one  wave-length  is  used,  as  is  approximately  the  case 
when  we  interpose  the  red  glass.  But  if  white  light,  or  light 
of  various  wave-lengths  is  used,  it  will  happen  that  those 
places  which  are  deprived  of  red  light  will  receive  light  of 
other  colors  ;  hence  the  color  effects  produced  when  white  light 
passes  through  the  ruled  glass.  Of  course  waves  are  generated 
at  the  points  G  and  N,  as  well  as  at  the  points  H  and  M,  but 
they  are  omitted  for  the  sake  of  simplicity.  This  figure  illus- 
trates only  in  a  very  incomplete  way  the  complex  phenomena. 


382  RADIANT    ENERGY.  —  LIGHT. 

Such  experiments  as  the  above  furnish  a  very  strong  argument 
for  the  wave  theory  of  light,  since  two  lights  produce  darkness 
apparently  in  a  manner  analogous  to  that  in  which  two  sounds 
produce  silence. 

Thin,  transparent  films  of  varying  thickness,  such  as  the  film 
of  a  soap  bubble,  are  well  suited  to  show  the  effects  of  inter- 
ference of  light.  Some  of  the  light  which  strikes  the  anterior 
surface  of  the  film  is  reflected  ;  another  portion  enters  the  film, 
and  is  reflected  from  the  posterior  surface ;  but,  by  travelling 
twice  through  the  film,  the  wave  loses  ground,  so  that,  on  emer- 
gence, its  phases  may  or  may  not  correspond  with  the  phases 
of  the  former  portion :  this  will  depend  evidently  upon  the 
thickness  of  the  film  at  a  given  point,  and  the  length  of  the 
waves  striking  that  point.  In  this  manner  the  phenomena  ob- 
tained in  the  first  experiment  are  explained ;  the  film  in  this 
case  is  the  layer  of  air  between  the  two  surfaces  of  glass. 

Colors  are  produced  by  reflection  from  the  surfaces  of  thin  transpar- 
ent films  of  all  kinds ;  for  example,  the  colors  of  the  soap  bubble,  of  oil 
on  water,  of  the  thin  coating  of  metallic  oxide  formed  in  tempering 
steel,  the  changeable  colors  of  the  peacock's  feathers  and  of  certain 
insects'  wings,  the  colors  seen  in  cracks  in  glass  and  ice,  are  all  colors 
of  thin  films.  The  halos  seen  around  the  moon  or  a  street  lamp  on  a 
misty  evening,  and  the  rainbow  tints  seen  bordering  the  eyelashes 
when,  with  eyes  partially  closed,  you  look  at  a  strong  light,  are  exam- 
ples of  colors  produced  by  diffraction. 

Waves  of  light  which  emanate  from  the  points  H  and  M, 
Figure  283,  travel  equal  distances  to  reach  the  point  i  on  the 
screen  ;  but  to  reach  the  point  #,  the  waves  from  H  must  travel 
just  one-half  of  a  wave-length  farther  than  the  waves  from  M  ; 
and  to  reach  the  point  J,  they  must  travel  just  one  wave-length 
farther.  Hence,  if  we  can  ascertain  the  difference  between  the 
two  distances,  Hg  and  M^,  we  obtain  the  wave-length  for  that 
color.  In  this  manner  the-  wave-lengths  given  in  §  336  were 
ascertained. 


DOUBLE    REFRACTION. 


383 


LVII1. 


DOUBLE    REFRACTION    AND    POLARIZATION    OF 
LIGHT. 


Fig.  285. 


§  352.  Double  refraction.  —Experiment.  Through  a  card 
make  a  pin-hole,  and  hold  the  card  so  that  you  may  see  skylight  through 
the  hole.  Now  bring  a  crystal  of  Iceland  spar,  Figure  284,  between 
the  eye  and  the  card, 
and  look  at  the  hole 
through  two  parallel 
surfaces  of  the  crys- 
tal. There  will  appear 
to  be  two  holes,  with 
light  shining  through 
each.  Cause  the  crys- 
tal to  rotate  in  a  plane 
parallel  with  the  card, 
and  one  of  the  holes 
will  appear  to  remain  nearly  at  rest,  while  the  other  rotates  around  the 
first.  A  ray  of  light  na  immediately  on  entering  the  crystal  is  divided 
into  two  parts,  one  of  which  obeys  the  regular  law  of  refraction;  the 
other  does  not.  The  former  is  called  the  ordinary  ray  /  the  latter,  the 
extraordinary  ray.  The  rays  issue  from  the  crystal  parallel  with  one 
another.  In  all  crystals  which  produce  this  phenomenon  there  is  one 
direction,  and  in  some  two  directions,  in  which,  if  an  object  is  looked 
at  through  the  crystal,  it  does  not  appear  double.  If  all  the  edges 
of  a  crystal  of  Iceland  spar  are  equal,  and  it  is  cut  by  two  planes  near 
each  extremity  of  the  line  AB,  which  connects  the  two  opposite  solid 
obtuse  angles,  and  at  right  angles  to  it,  as  shown  in  Figure  285,  ob- 
jects viewed  in  this  line,  or  in  any  line  parallel  with  it,  do  not  appear 
double. 

In  every  direction  in  which  one  looks  through  the  crystal, 
except  parallel  to  AB,  objects  seen  through  it  appear  double. 


Fig.  286. 


(See  Fig.  286.)      The  line  AB  is  called 

the  optic  axis  of  the  crystal,  and  is  a  line 

around  which  the  molecules  of  the  crystal 

appear  to  be  arranged  symmetrically.     A 

crystal  is  called  uniaxial  when  it  has  only 

one  optic  axis,  and  biaxial  when  it  has  two  such  axes.    Crystals 

of  many  other  substances  possess  the  property  of  causing  objects 


384 


RADIANT    ENERGY.  —  LIGHT. 


seen  through  them  to  appear  double. 
double  refraction. 


This  phenomenon  is  called 


Fig.  287. 


Fig.  288. 


§  353.    Polarization.  —  Slices   of  crystals   of  the   mineral 
tourmaline,  cut  in  planes  parallel  with  their  axes,  are  prepared 
and  sold  for  optical  experiments.     If  two  of  these  slices  simi- 
larly  situated,    as   in 
Figure  287,  are  placed 
between  the  eye  and  a 
card  pierced  by  a  hole, 
the  hole  will  be  plainly 
visible.     But  if  one  of 
the  slices  is  slowly  rotated  in  a  plane  at  right  angles  with  the 
Fig.  289.  beam  of  light,  the   hole 

|B  will  grow  dimmer  until  the 
slice  has  passed  through 
a  quarter  of  a  revolution 
(as  represented  in  Figure 
If  the  rotation  is  continued,  the  hole 
reappears,  faint  at  first,  but  at  the  end  of  another  quarter- 
revolution  it  reaches  its  maximum  brightness.  Thus,  at  each 
quarter-revolution  it  is  alternately  extinguished  and  restored. 

It  appears,  then,  that  light  which  has  passed  through  one 
transparent  slice  of  tourmaline  differs  so  much  from  common 
light,  that  a  second  similar  slice  may  act  like  an  opaque  body, 
and  stop  it  altogether.  The  action  of  the  tourmaline  may  be 
compared  to  that  of  a  grating  (A,  Fig.  289)  formed  of  parallel 
vertical  rods,  which  will  allow  all  vertical  planes  (as  aa')  to  pass, 
but  stops  the  planes  (as  cc')  that  are  at  right  angles  to  these  rods. 
Any  plane  that  has  succeeded  in  passing  one  grating  will  readily 
pass  a  second  similarly  placed.  But  if  the  second  grating  B  is 
turned  so  that  its  rods  are  at  right  angles  to  the  first,  the  plane 
that  has  succeeded  in  getting  through  the  first  grating  will  be 
stopped  by  the  second.  Light,  in  this  condition,  is  said  to  be 
polarized;  polarization  is  either  the  act  of  producing  the  change 


288),  when  it  disappears. 


POLARIZATION. 


386 


in  the  light,  or  the  result  of  the  change,  and  the  instrument  used 
is  a  polarizer. 

In  order  to  understand  this  phenomenon,  it  is  necessary  to 
know  more  of  the  un-  Fig.  200. 

dulatory  theory  of  light. 
This  theory  supposes 
that  the  undulations  in 
ether  which  constitute 
light  are  much  like  undulations  in  a  cord  when  one  end  is  shaken 
by  a  hand,  as  seen  in  Figure  290.  If  the  hand  moves  vertically, 
all  the  undulations  will  lie  in  a  vertical  plane  ;  if  the  movements 
of  the  hand  are  horizontal  or  oblique,  the  undulations  lie  in 
corresponding  planes.  So  we  can  produce  these  waves  on  the 
rope  in  any  plane  passing  through  the  rope,  and  can  change 
rapidly  from  one  plane  to  another.  These  waves  appear  differ- 
ently when  viewed  from  different  sides.  If  we  could  look  end- 
wise at  a  ray  of  light  for  an  instant,  it  is  believed  that  we  should 
see  the  ether  particles  vibrating,  as  in  the  figure  of  the  rope,  in 

Fig.  291. 


ono  plane  ;  but  in  only  a  thousandth  of  a  second  so  many  million 
waves  reach  the  eye,  that  there  is  time  for  the  vibrating  par- 
ticles, which,  like  the  hand,  start  the  waves,  to  vibrate  in  many 
planes.  In  an  ordinary  beam  of  light,  as  it  reaches  the  eye, 
there  are  therefore  undulations  in  all  possible  planes,  as  is  par- 
tially represented  by  the  cross  section  A,  Figure  291.  But  any 
motion  may  be  considered  as  the  effect  of  two  forces  that  would 
produce  motions  in  directions  at  right  angles  to  one  another. 
So  here,  for  many  practical  purposes,  the  vibrations  may  be 
regarded  as  taking  place  in  only  two  sets  of  planes  at  right 


386  KADIANT    ENERGY.  —  LIGHT. 

angles  to  one  another,  as  represented  by  B  of  the  same  figure. 
Now,  when  a  ray  of  light,  consisting,  according  to  supposition,  of 
undulations  in  planes  at  right  angles  to  one  another,  strikes  a  slice 
of  tourmaline,  its  molecular  structure  allows  those  undulations 
which  are  in  planes  parallel  with  its  axis  to  pass  through,  but 
it  absorbs  those  undulations  that  are  in  planes  at  right  angles 
to  its  axis.  By  this  means  the  undulations  are  reduced  to  those 
•in  parallel  planes  only,  as  represented  in  C.  The  unaided  eye 
cannot  usually  detect  any  difference  between  common  and  polar- 
ized light.  An  instrument  which  will  enable  the  eye  to  detect 
polarized  light  is  called  an  analyzer ;  thus  the  first  slice  of  tour- 
maline serves  as  a  polarizer,  and  the  second  slice  as  an  analyzer. 
A  complete  polarizing  apparatus,  called  a  polar iscope,  used  for 
Fig.  292.  observing  the  phenom- 

ena of  polarized  light, 
consists  essentially  of  a 
polarizer  and  an  ana- 
lyzer. 

The  favorite  analyzer  is 
the  Nicol  prism,  which  consists  of  a  crystal  of  Iceland  spar  divided 
diagonally,  as  AB,  Figure  292,  and  the  two  surfaces  cemented  together 
again  with  Canada  balsam.  The  extraordinary  ray  CE,  falling  upon  the 
transparent  balsam,  passes  through  it ;  but  the  ordinary  ray  CN  strikes 
the  balsam  at  a  greater  than  its  critical  angle,  and  is  therefore  reflected 
out  of  the  crystal,  and  thus  got  rid  of.  Now,  when  polarized  light 
enters  this  prism  in  one  position,  it  will  pass  freely  through  it,  but  if 
the  prism  is  turned  90°,  none  will  pass  through.  In  the  example  given 
above,  light  is  polarized  by  absorption. 

§  354.  Polarization  by  double  refraction  and  by  reflec- 
tion. —  If  light  which  has  undergone  double  refraction,  as  in 
passing  through  a  crystal  of  Iceland  spar,  is  examined  with  an 
analyzer,  it  is  found  that  both  the  ordinary  and  the  extraordi- 
nary rays  are  completely  polarized  in  planes  at  right  angles  to 
each  other.  Again,  light  reflected  obliquely  from  smooth  sur- 
faces, such  as  water,  glass,  and  polished  furniture,  etc.,  is  found 


DESCRIPTION   OF   A   SIMPLE   POLARISCOPE. 


387 


Fig.  293. 


on  examination  to  be  partially  polarized.  There  is  a  definite 
angle  of  incidence  at  which  the  maximum  polarizing  effects  are 
produced.  This  angle  varies  with  different  substances.  With 
glass  it  is  55°  ;  with  water,  53°. 

§  355.  Description  of  a  simple  polariscope.  —  D  (Fig.  293) 
is  a  plate  of  glass,  about  15cm  square,  used  as  a  polarizer.  A  is  the 
analyzer,  —  preferably  a  Nicol 
prism,  —  so  placed  as  to  view  the 
center  of  the  glass  at  the  proper 
polarizing  angle  (about  55°).  The 
prism  may  be  mounted  in  a  cork, 
and  the  whole  should  be  free  to 
rotate  in  its  support.  S  is  a  piece 
of  ground  glass  used  to  cut  off  s 
the  images  of  outside  objects.  G 
is  a  glass  shelf,  on  which  objects 
to  be  examined  are  placed.  The 
instrument,  covered  with  a  black  cloth,  is  placed  on  a  table  with  S 
toward  a  window.  The  prism  can  be  obtained  of  any  dealer  in  optical 
apparatus. 

§  356.  Colors  by  polarization.  — Experiment.  Place  on  the 
support  G  a  thin  film  of  selenite  or  mica,  and  slowly  rotate  the  analyzer. 
A  beautiful  display  of  colors  will  appear.  At  a  certain  point  they  will 
appear  of  maximum  brilliancy,  then  they  will  gradually  fade  away  and 
change  into  their  complementaries. 

This  is  really  a  phenomenon  of  interference,  brought  about 
through  the  combined  agency  of  the  object  examined  and  the 
polariscope.  If  a  piece  of  plate  glass,  subjected  to  pressure  by 
means  of  a  screw-clamp,  or  a  piece  of  unannealed  or  poorly 
annealed  glass,  —  a  glass  stopper,  for  example,  —  is  examined, 
it  will  exhibit  analogous  phenomena. 


888  RADIANT    ENERGY.  —  LIGHT. 


LIX.     THERMAL  EFFECTS   OF   RADIATION. 

§  357.  Diathermancy  and  athermancy. — What  becomes 
of  radiations  that  strike  a  body  depends  largely  upon  the  char- 
acter of  the  body.  If  the  nature-  of  the  body  is  such  that  its 
molecules  can  accept  the  motion  of  the  ether,  the  undulations 
of  ether  are  said  to  be  absorbed  by  the  body,  and  the  body  is 
thereby  heated ;  that  is,  the  undulations  of  ether  are  trans- 
formed into  molecular  motion  or  heat.  A  good  illustration  of 
this  is  the  experiment  with  blackened  glass,  page  325.  On  the 
other  hand,  the  unblackened  glass  allows  the  radiations  to  pass 
freely  through  it,  and  very  little  is  transformed  into  heat. 
Notice  how  cold  window-glass  ma3r  remain,  while  radiations 
pour  through  it  and  heat  objects  within  the  room.  It  must  be 
constantly  borne  in  mind,  that  only  those  radiations  that  a  body 
absorbs  heat  it;  those  that  pass  through  it  do  not  affect  its  tem- 
perature. Bodies  that  transmit  radiant  heat  freely  are  said  to 
be  diathermanous,  while  those  that  absorb  it  largely  are  called 
athermanous.  The  most  diathermanous  solid  is  rock  salt. 
Among  the  most  athermanous.  solids  are  lamp-black  and  alum. 
Carbon  bisulphide,  among  liquids,  is  exceptionally  transparent 
to  all  forms  of  radiation;  while  water,  transparent  to  short 
waves,  absorbs  the  longer  waves,  and  is  thus  quite  athermanous. 

Experiment  1.  Bring  the  bulb  of  an  air  thermometer  into  the 
focus  of  a  burning-glass  exposed  to  the  sun's  rays.  The  radiation 
concentrated  on  the  enclosed  air  scarcely  affects  this  delicate  instru- 
ment. 

Experiment  2.  Cover  the  outside  of  the  bulb  of  the  air  thermom- 
eter with  lamp-black  and  repeat  the  last  experiment.  The  lamp-black 
absorbs  the  radiant  heat,  and  the  heat  conducted  through  the  glass  to 
the  enclosed  air  raises  its  temperature  and  causes  it  to  expand  and 
rapidly  push  the  liquid  out  of  the  stem. 

Dry  air  is  almost  perfectly  diathermanous.  All  of  the  sun's 
radiations  that  reach  the  earth  pass  through  a  layer  of  air,  from 
fifty  to  two  hundred  miles  in  depth,  which  contains  a  vast 


DIATHEEMANCY   AND   ATHERMANCY.  389 

amount  of  aqueous  vapor.  This  vapor,  like  water,  is  compara- 
tively opaque  to  long  waves ;  hence  it  modifies  very  much  the 
character  of  the  radiations  which  reach  the  earth.  This  fact, 
together  with  what  we  have  learned  from  Exp.  2,  enable  us 
to  understand  the  method  by  which  our  atmosphere  becomes 
heated.  First,  a  very  considerable  portion  of  the  radiant  energy 
which  comes  to  us  from  the  sun,  in  the  form  of  relatively  long 
waves,  is  stopped  by  the  watery  vapor  in  the  air,  which  is,  in 
consequence,  heated.  Most  of  that  which  escapes  this  absorp- 
tion heats  the  earth  by  falling  upon  it.  The  warmed  earth  loses 
its  heat,  —  partly  by  conduction  to  the  air,  still  more  largely  by 
radiation  outward.  The  form  of  radiation,  however,  has  been 
greatly  changed ;  for  now,  coming  from  a  body  at  a  low  temper- 
ature, it  is  chiefly  in  long  waves  that  the  energy  is  transmitted ; 
while,  as  we  have  seen,  it  was  largely  in  the  form  of  short  waves 
that  the  earth  received  its  heat.  But  it  is  exactly  these  long 
waves  which  are  most  readily  stopped  by  the  atmosphere  ;  hence, 
the  atmosphere,  or  rather  the  aqueous  vapor  of  the  atmosphere, 
acts  as  a  sort  of  trap  for  the  energy  which  comes  to  us  from  the 
sun.  Remove  the  watery  vapor  (which  serves  as  a  "  blanket " 
to  the  earth)  from  our  atmosphere,  and  the  chill  resulting  from 
the  rapid  escape  of  heat  by  radiation  would  put  an  end  to  all 
animal  and  vegetable  life.  Glass  does  not  screen  us  from  the 
sun's  heat,  but  it  can  very  effectually  screen  us  from  the  heat 
radiated  from  a  stove  or  any  other  terrestrial  object.  Glass  is 
diathermanous  to  the  sun's  radiations  (simply  because  they 
have  already  lost  most  of  the  very  long  waves  by  atmospheric 
absorption) ,  but  quite  athermanous  to  other  radiations.  This 
is  well  illustrated  in  the  case  of  hot-beds  and  green-houses. 
The  sun's  heat  passes  through  the  glass  of  these  enclosures, 
almost  unobstructed,  and  heats  the  earth ;  but  the  radiations 
given  out  in  turn  by  the  earth  are  such  as  cannot  pass  out 
through  the  glass,  hence  the  heat  is  retained  within  the  enclo- 
sures. 


390  RADIANT    ENERGY.  — -  LIGHT. 

§  358.  All  bodies  radiate  heat.  —  Hot  bodies  usually  part 
with  their  heat  much  more  rapidly  by  radiation  than  by  all  other 
processes  combined.  But  cold  bodies,  like  ice,  radiate  heat  even 
when  surrounded  by  warm  bodies.  This  must  be  so  from  the 
nature  of  the  case,  for  the  molecules  of  the  coldest  bodies 
possess  some  motion,  and  being  surrounded  by  ether,  they  can- 
not move  without  imparting  some  of  their  motion  to  the  ether, 
and  to  that  extent  become  themselves  colder. 

§  359.  Theory  of  Exchanges.  —  Let  us  suppose  that  we 
have  two  bodies,  A  and  B,  at  different  temperatures,  — A  warmer 
than  B.  Radiation  takes  place  not  only  from  A  to  B,  but  from 
B  to  A  ;  but,  in  consequence  of  A's  excess  of  temperature,  more 
heat  passes  from  A  to  B  than  from  B  to  A,  and  this  continues 
until  both  bodies  acquire  the  same  temperature.  At  this  point 
radiation  by  no  means  ceases,  but  each  now  gives  as  much  as  it 
receives,  and  thus  equilibrium  is  kept  up.  This  is  known  as 
the  "  Theory  of  Exchanges." 

§  360.   Good  absorbers,  good  radiators.  —  Experiment. 

Select  two  small  tin  boxes  of  equal  capacity,  —  one  should  be  bright  out- 
side, while  the  other  should  be  covered  thinly  with  soot  from  a  candle 
flame.  Cut  a  hole  in  the  cover  of  each  box  large  enough  to  admit  the 
bulb  of  a  thermometer.  Fill  both  boxes  with  hot  water,  and  introduce 
into  each  a  thermometer.  They  will  register  the  same  temperature  at 
first.  Set  both  in  a  cool  place,  and  in  half  an  hour  you  will  find  that 
the  thermometer  in  the  blackened  box  registers  several  degrees  lower 
than  the  other.  Then  fill  both  with  cold  water,  and  set  them  in  front 
of  a  fire  or  in  the  sunshine,  and  it  will  be  found  that  the  temperature 
in  the  blackened  box  rises  fastest. 

As  bodies  differ  widely  in  their  absorbing  power,  so  they  do 
in  their  radiating  power,  and  it  is  found  to  be  universally  true 
that  good  absorbers  are  good  radiators,  and  bad  absorbers  are 
bad  radiators.  Much,  in  both  cases,  depends  upon  the  charac- 
ter of  the  surface  as  well  as  the  substance.  Bright,  polished 
surfaces  are  poor  absorbers  and  poor  radiators  ;  while  tarnished, 
dark,  and  roughened  surfaces  absorb  and  radiate  heat  rapidly. 


COMPOUND   MICROSCOPE.  391 

Dark  clothing  absorbs  and  radiates  heat  more  rapidly  than  light. 
(Which  is  better  to  wear  at  all  seasons  ?  Why  ?  Why  are  cer- 
tain parts  of  steam  engines  kept  scrupulously  bright?  ) 

§  361.  Dew.  —  It  requires  no  elaborate  experiments  to  show 
that  some  bodies  radiate  heat  more  rapidly  than  others.  All 
nature  testifies  to  this  every  still,  cloudless  summer  night.  Dur- 
ing the  day  objects  on  the  earth's  surface  receive  more  heat  by 
radiation  than  they  lose,  but  as  soon  as  the  sun  has  set  this 
is  reversed.  Then  everything  begins  to  cool  as  its  heat  is  radi- 
ated into  space.  Objects  becoming  cool,  the  air  in  contact  with 
them  becomes  chilled  ;  its  watery  vapor  condenses,  and  collects 
in  tiny  liquid  drops  on  their  surfaces.  But  these  dew-drops 
collect  much  more  abundantly  on  certain  things,  such  as  grasses 
and  leaves,  than  on  others,  such  as  stones  and  earth.  The 
reason  that  it  does  not  collect  on  the  latter  so  freely,  is  because 
of  their  poor  radiating  power ;  they  do  not  get  cool  as  rapidly. 

Fig.  294. 


LX.     SOME   OPTICAL   INSTRUMENTS. 

§362.  Compound,  microscope. —The  simple  microscope 
was  described  on  page  362.  When  it  is  desired  to  magnify  an 
object  more  than  can  be  done  conveniently  and  with  distinct- 
ness by  a  single  lens,  two  convex  lenses  are  used,  —  one  (O, 
Fig.  294)  called  the  object-glass,  to  form  a  magnified  real  image 


392  BADIANT  ENERGY.  —  LIGHT. 

A'B'  of  the  object  AB  ;  and  the  other  (E)  called  the  eye-glass, 
to  magnify  this  image  so  that  the  image  A'B'  appears  of  the  size 
A"B".  In  the  same  sense  as  we  look  at  the  object  with  one 
lens  when  we  use  a  simple  microscope,  here  we  look  at  A'B'. 

§  363.  Astronomical  telescope.  —  The  astronomical  re- 
fracting telescope  consists  essentially,  like  the  compound  micro- 
scope, of  two  lenses.  The  object-glass  (O,  Fig.  295)  forms  a 
real  diminished  image  db  of  the  object  AB ;  this  image,  seen 
through  the  eye-glass  E,  appears  magnified  and  of  the  size  cd. 
The  object-glass  is  of  large  diameter,  in  order  to  collect  as 
much  light  as  possible  from  a  distant  object  for  a  better  illumi- 
nation of  the  image.  Some  idea  of  the  power  of  some  of  our 

Fig.  295. 


best  telescopes  may  be  obtained  from  the  fact  that  Mr.  Clark 
of  Cambridgeport  has  made  a  telescope  of  such  magnifying 
power,  and  possessing  such  distinctness  of  definition,  that  a  ball 
two  inches  in  diameter,  and  two  hundred  and  fifty  miles  distant 
(about  the  distance  between  Boston  and  New  York) ,  would  be 
distinctly  visible  as  a  body  of  perceptible  dimensions,  if  properly 
illuminated. 

§  364.  Photographer's  camera.  —  The  photographer's  cam- 
era, or  camera  obscura,  of  which  AB,  Figure  296,  represents  a 
vertical  section,  consists  of  a  dark  box  painted  black  on  the 
interior.  A  screen  of  ground  glass  S  forms  a  partition  in  the 


THE   HUMAN   EYE. 


393 


box.  A  sliding  tube  T  contains  a  convex  lens  L.  If  an  object 
D  is  placed  some  distance  in  front,  and  the  distance  of  the  lens 
from  the  screen  is  suitably  adjusted,  a  distinct,  real,  and  inverted 
image  can  be  seen  upon  the  screen  by  looking  through  the 
aperture  C.  When  the  image  is  properly  focused,  the  photo- 
grapher replaces  the  ground  glass  plate  by  a  sensitized  plate, 
and  the  chemical  power  of  the  sun's  rays  paints  a  true  picture 
of  the  object  on  this  plate. 

Fig.  296. 


Fig.  297. 


§  365.  The  human  eye.  —  Figure  297  represents  a  horizontal 
section  of  this  wonderful  organ.  Covering  the  front  of  the  eye,  like  a 
watch-crystal,  is  a  transparent  coat  1, 
called  the  cornea.  A  tough  membrane 
2,  of  which  the  cornea  is  a  continua-< 
tion,  forms  the  outer  wall  of  the  eye, 
and  is  called  the  sclerotic  coat,  or 
"  white  of  the  eye."  This  coat  is 
lined  on  the  interior  with  a  delicate 
membrane  3,  called  the  choroid  coat ; 
the  latter  is  covered  with  a  black 
pigment,  which  prevents  internal 
reflection.  The  inmost  coat  4,  called 
the  retina,  is  formed  by  expansion 
of  the  optic  nerve  O.  The  front  of 
the  choroid  coat  ii  is  called  the  iris  ; 
its  color  constitutes  the  so-called 

"color  of  the  eye."  In  the  center  of  the  iris  is  a  circular  opening  5, 
called  the  pupil,  whose  function  is  to  regulate,  by  involuntary  enlarge- 
ment and  contraction,  the  quantity  of  light  admitted  to  the  interior 
chamber  of  the  eye.  Just  back  of  the  iris  is  a  tough,  elastic,  and 
transparent  body  0,  called  the  crystalline  lens.  This  lens  divides  the 


394  RADIANT   ENERGY.  —  LIGHT. 

eye  into  two  chambers ;  the  anterior  chamber  7  is  filled  with  a  limpid 
liquid,  called  the  aqueous  humor;  the  posterior  chamber  8  is  filled  with 
a  jelly-like  substance,  called  the  vitreous  humor. 

The  eye  is  a  camera  obscura,  in  which  the  retina  serves  as  a 
screen.  Images  of  outside  objects  are  projected  by  means  of 
the  crystalline  lens,  assisted  by  the  refractive  powers  of  the 
humors,  upon  this  screen,  and  the  impressions  thereby  made  on 
this  delicate  network  of  nerve  filaments  are  conveyed  by  the 
optic  nerve  to  the  brain.  If  the  two  outer  coatings  are  removed 
from  the  back  part  of  the  eye  of  an  ox,  recently  killed,  so  as  to 
render  it  somewhat  transparent,  true  images  of  wholo  land- 
scapes may  be  seen  formed  upon  the  retina  of  the  eye,  when  it 
is  held  in  front  of  your  eye.  With  the  ordinary  camera,  the 
distance  of  the  lens  from  the  screen  must  be  regulated  to  adapt 
itself  to  the  varying  distances  of  outside  objects,  in  order  that 
the  images  may  be  properly  focused  on  the  screen.  In  the  eye 
this  is  accomplished  by  changing  the  convexity  of  the  lens.  We 
can  almost  instantly  and  involuntarily  change  the  lens  of  the 
eye,  so  as  to  form  on  the  retina  a  distinct  image  of  an  object 
miles  away  or  only  a  few  inches  distant.  The  nearest  limit  at 
which  an  object  can  be  placed,  and  form  a  distinct  image  on  the 
retina,  is  about  five  inches.  On  the  other  hand,  the  normal  eye 
in  a  passive  state  is  adjusted  for  objects  at  an  infinite  distance. 
Curious  enough,  the  retina  on  careful  examination  is  found  to 
be  covered  with  little  projections  which  have  received,  from 
their  appearance,  the  names  of  rods  and  cones.  These  project 
from  the  nerve  fibres  very  much  like  nap  from  the  threads  of 
velvet.  It  is  thought  that  these  rods  and  cones  receive  and 
respond  to  the  vibrations  of  light ;  in  other  words,  that  they 
co-vibrate  with  the  undulations  of  the  ether,  and  thereby  we  get 
our  sensation  of  light. 

§  366.  Chromatic  aberration.  —  There  is  a  serious  defect 
in  ordinary  convex  lenses,  to  which  we  have  not  before  alluded, 
called  chromatic  aberration,  which  has  required  the  highest  skill 


STEREOPTICON. 


395 


of  man  to  correct.  The  convex  lens  both  refracts  and  disperses 
the  light  that  passes  through  it.  The  tendency,  of  course,  is  to 
bring  the  more  refrangible  rays,  as  the  violet,  to  a  focus  much 
sooner  than  the  less  refrangible  rays,  such  as  the  red.  The 
result  is  a  disagreeable  coloration  of  the  images  that  are  formed 
by  the  lens,  especially  by  that  portion  of  the  light  that  passes 
through  the  lens  near  its  edges.  This  evil  has  been  overcome 
very  effectually  by  combining  with  the  convex  lens  a  plano-con- 
cave lens.  Now,  if  a  crown-glass  convex  lens  is  taken,  Fig.  298. 
a  flint-glass  concave  lens  may  be  prepared  that  will 
correct  the  dispersion  of  the  former  without  neutralizing 
all  its  refraction.1  A  compound  lens,  composed  of  these 
two  lenses  (Fig.  298)  cemented  together,  constitutes  what 
is  called  an  achromatic  lens. 

Fig.  299. 


§367.  Stereopticon. — This  instrument  is  extensively  em- 
ployed in  the  lecture-room  for  producing  on  a  screen  magnified 
images  of  small  transparent  pictures  on  glass,  called  slides; 
also  for  rendering  a  certain  class  of  experiments  visible  to  a 
large  audience  by  projecting  them  on  a  screen.  The  light  most 
commonly  used  is  the  lime  light,  though  the  electric  light  is  pre- 
ferred for  a  certain  class  of  projections.  The  flame  of  an  oxyhy- 
drogen  blow-pipe  A,  Figure  299,  is  directed  against  a  stick  of 
lime  B,  and  raises  it  to  a  white  heat.  The  light  of  the  lime  is 
converged  —  by  means  of  a  convex  lens  c,  called  the  condensing 
lens  (usually  two  plano-convex  lenses  are  used)  —  upon  the  slide 

1  The  refractive  and  dispersive  powers  of  the  two  lenses  are  not  proportional. 


396  RADIANT    ENERGY.  —  LIGHT. 

D,  and  strongly  illuminates  it.  In  front  of  it  is  placed  another 
convex  lens  E  (or  a  system  of  lenses) ,  called  the  projecting  lens. 
The  latter  lens  produces  (or  projects)  a  real,  inverted,  and 
magnified  image  of  the  picture  on  the  screen  S»  The  mounted 
lens  E  may  be  slid  back  and  forth  on  the  bar  F,  so  as  properly 
to  focus  the  image.  (For  useful  information  relating  to  the 
operation  of  projection,  see  Dolbear's  Art  of  Projection.) 


APPENDIX, 


Inches. 


[7 \S _J9 10 


Millimeters 


The  area  of  this  figure  Is  a  square  decimeter. 
A  cube  of  water,  one  of  whose  sides  is  this  area, 
is  a  cubic  decimeter  or  a  liter  of  water,  and  at  the 
temperature  of  4°  C.  weighs  a  kilogram.  The 
same  volume  of  air  at  0°  C.,  and  under  a  pressure 
of  one  atmosphere,  weighs  1.293  grams.  The 
gram  is  the  weight  of  lcc  of  pure  water  at  4°  C. 


Square    ; 
Centimeter; 


Square  Inch. 


398 


APPENDIX. 


401 


SECTION  B. 

Cutting  glass. —  Bottoms  of  glass  bottles  may  be  cut  off,  and 
plate  glass  may  be  easily  cut  in  any  pattern  desirable,  by  observing  the 
following  directions.  Procure  an  iron  rod  B,  Fig.  300,  25cm  long  and 
7mm  m  diameter,  and  insert  one-end  in  a  wooden  handle  C,  and  let  the 
exposed  end  be  filed  to  a  smooth  surface.  With  a  pointed  piece  of  soap, 
trace  a  line  on  the  glass  where  you  would  cut ;  and,  if  it  is  a  bottle 
that  is  to  be  cut,  file  a  short  gash  A  (to  a  depth  varying  with  the  thick- 
ness of  the  glass) 
in  the  bottle  in  the 
direction  of  the 
line  drawn.  Heat, 
in  a  Bunsen  flame, 
the  free  end  of  the 


Fig.  300. 


rod  to  a  bright  red 
heat  (the  hotter 
the  better),  and 
apply  the  heated 
end  to  the  glass,  as 

in  the  figure,  about  lmm  from  one  extremity  of  the  gash  for  (say)  about 
five  seconds  (longer  if  the  glass  is  very  thick ;  not,  however,  long  enough 
to  crack  the  glass),  and  then  quickly  apply  it  in  the  same  manner  to 
the  other  extremity  of  the  gash,  as  D,  and  hold  it  firmly  till  you  see 
a  fine  crack  creeping  toward  the  rod ;  then  slowly  move  the  rod  along 
the  traced  line,  and  the  crack  will  follow  faithfully  the  movements 
of  the  rod.  If  plate  glass  is  to  be  cut,  file  a  small  gash  E  in  one 
edge ;  and,  commencing  with  this  gash  as  before,  you  may  cut  in  the 
glass  a  circle,  or  any  design  you  desire.  To  bore  holes  in  glass,  make 
a  thick  paste  by  partially  dissolving  gum  camphor  in  spirits  of  tur- 
pentine ;  nip  off  a  short  piece  from  the  end  of  a  small  rat-tail  file, 
and,  keeping  the  ragged  end  wet  with  the  paste,  you  can  readily  bore 
a  hole  by  employing  strong  pressure,  and  by  a  twisting  movement  as 
in  boring. 


402 


APPENDIX. 


SECTION   C. 

TABLES    OF   SPECIFIC    GRAVITIES    OF   BODIES. 

[The  standard  employed  in  the  tables  of  solids  and  liquids  is  distilled  water  at  4"  C.] 

I.   Solids. 


Antimony 6.712 

Bismuth 9.822 

Brass 8.380 

Copper,  cast 8.790 

Iridium 23.000 

Iron,  cast 7.210 

Iron,  bar 7.780 

Gold 19.360 

Lead,  cast 1 1.350 

Platinum 22.069 

Silver,  cast 10.470 

Tiu,cast.... 7.290 

Zinc,  cast 6.860 

Anthracite  coal 1.800 

Bituminous  coal ..  1.250 


Diamond 3.530 

Glass,  flint 3.400 

Human  body 0.890 

Ice 0.920 

Quartz 2.650 

Kock  salt 2.257 

Saltpetre 1.900 

Sulphur,  native 2.033 

Tallow 0.942 

Wax 0.969 

Cork 0.240 

Pine 0.650 

Oak 0.845 

Beech 0.852 

Ebony 1.187 


II.    Liquids. 


Alcohol,  absolute 

Bisulphide  of  carbon .  . . 

Ether 

Hydrochloric  acid 

Mercury 

Milk 

Naphtha 


0.800 
1.293 
0.723 
1.240 
13.598 
1.032 
0.847 


Nitric  acid 1.420 

Oil  of  turpentine 0.870 

Olive  oil 0.915 

Sea  water 1.026 

Sulphuric  acid 1.841 

Water,  4°  C. ,  distilled ...  1 .000 

Water,  0°  C. ,  distilled . . .  0.999 


III.    Gases. 

[Standard:  airatO°C.;  barometer,  76«m.j 


Air 1.0000 

Ammonia 0.5367 

Carbonic  acid 1.5290 

Chlorine 3.4400 

Hydrochloric  acid 1.2540 


Hydrogen 0.0693 

Nitrogen 0.9714 

Oxygen 1. 1057 

Sulphuretted  hydrogen ..  1.1912 
Sulphurous  acid 2.2474 


APPENDIX. 


403 


SECTION   D. 

TABLE  OF  NATURAL  TANGENTS. 


Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

Deg. 

Tangent. 

1 

.017 

24 

.445 

47 

1.07 

70 

2.75 

2 

.035 

25 

.466 

48 

1.11 

71 

2.90 

3 

.052 

26 

.488 

49 

1.15 

72 

3.08 

4 

.070 

27 

.510 

50 

1.19 

73 

3.27 

5 

.087 

28 

.532 

51 

1.23 

74 

3.49 

6 

.105 

29 

.554 

52 

1.28 

75 

3.73 

7 

.123 

30 

.577 

53 

1.33 

76 

4.01 

8 

.141 

31 

.601 

54 

1.38 

77 

4.33 

9 

.158 

32 

.625 

55 

1.43 

78 

4.70 

10 

.176 

33 

.649 

56 

1.48 

79 

5.14 

11 

.194 

34 

.675 

57 

1.54 

80 

5.67 

12 

.213 

35 

.700 

58 

1.60 

81 

6.31 

13 

.231 

36 

.727 

59 

1.66 

82 

7.12 

14 

.249 

37 

.754 

60 

1.73 

83 

8.14 

15 

.268 

38 

.781 

61 

1.80 

84 

9.51 

16 

.287 

39 

.810 

62 

1.88 

85 

11.43 

17 

.306 

40 

.839 

63 

1.96 

86 

14.30 

18 

.325 

41 

.869 

64 

2.05 

87 

19.08 

ID 

.344 

42 

.900 

65 

2.14 

88 

28.64 

20 

.364 

43 

.933 

66 

2.25 

89 

57.29 

21 

.384 

44 

.966 

67 

2.36 

90 

Infinite. 

22 

.404 

45 

1.000 

68 

2.48 

23 

.424 

46 

1.036 

69 

2.61 

404 


APPENDIX. 


SECTION   B. 

Galvanometer.  —  A  galvanometer  that  will  answer  sufficiently 
well  all  the  purposes  of  this  book  can  be  easily  and  cheaply  prepared 
as  foUows :  Make  a  wooden  frame  A  (Fig.  301),  10cm  square  and 
2.5cm  thick,  joined  by  wooden  or  brass  pins  in  grooves ;  on  it  wind  50 
to  60  turns  (|  Ib.)  insulated  No.  16  wire  in  three  layers,  leaving  lcm 
space  in  the  center  (in  the  figure  this  space  is  exaggerated  in  order 
to  show  the  position  of  the  needles),  and  insert  the  extremities  in  the 
brass  screw-cups  L  and  K.  In  this  frame  insert  a  copper  or  brass 
wire  D,  carrying  a  cork  E,  which  supports  a  silk  fibre  F  and  a  strip  of 

Fig.  301. 


paper  G.  Magnetize  a  large  sewing-needle  H,  and  insert  in  the  paper, 
as  in  the  figure ;  also  insert  a  small  copper  wire  I  in  the  paper  for  a 
pointer,  and  suspend  the  whole  so  that  the  needle  will  swing  freely 
between  the  upper  and  lower  windings  of  wire,  and  the  pointer  will  be 
just  above  the  coils.  Prepare  a  graduated  circle  on  a  card  M,  having 
a  hole  in  the  center  through  which  to  pass  the  needle,  and  lay  it  on  the 
coil.  To  prevent  disturbance  from  currents  of  air,  cover  the  whole 
with  a  frame  N,  having  a  glass  plate  O  laid  over  its  top.  Connect  the 
battery  wires  with  the  screw-cups  L  and  K.  The  cost  of  material  need 
not  exceed  75  cents. 


APPENDIX.  405 


SECTION  P. 

Kind  of  battery  to  use.  —  Several  things  must  be  considered 
in  the  selection  of  a  battery  for  a  particular  use.  Among  the  most 
important  of  these  are  the  intensity  of  current  required,  and  the 
service  required;  i.e.,  whether  continuous,  temporary,  or  occasional 
currents  are  wanted.  The  cost  is  of  consequence,  but  that  must  be 
governed  mainly  by  the  preceding  considerations.  In  the  following 
arrangement,  preferences  are  given  to  the  several  batteries  by  num- 
bers, in  the  order  in  which  they  occur  against  the  several  uses 
specified :  — 


NAMES    OF    BATTERIES,    ETC. 


1.  Smee. 

2.  Leclauche. 

3.  Gravity. 


4.  Daniell.  , 

5.  Grenet. 

6.  Bimsen  or  Grove. 


7.  Magneto    or    dy- 

namo machines. 

8.  Thermo-batteries. 


USES  CELLS  ARE  SUITED  FOR. 
Strong,  Continuous  Currents. 

Electrotyping  or  Electro-plating 7,  4,  1,  3. 

Electro-magnets 3,  4,  1. 

Electric  light 7,  6. 

Telegraph  (closed  circuit) 3,4. 

Temporary. 

Induction  coils 5,  6,  4,  3. 

Medical  coils 5,1. 

Occasional. 

Annunciators,  domestic  bells 2,  1,  3,  4. 

Exploding  fuses 2,4. 

Electrical  measurements  (constant  current) 8,  4,  3. 


\ 


406 


APPENDIX. 


SECTION   G. 

Apparatus  to  illustrate  wave-motion.  —  The  most  efficient 
apparatus  for  this  purpose  that  we  have  seen  may  be  constructed  as 
follows.  Procure  forty  wooden  return-balls  (sold  at  toy  stores)  ;  sus- 
pend them  by  strings  (better,  fine  wires)  about  lm  long,  as  in  Figure 
302,  and  about  7cm  apart.  Connect  all  the  balls  horizontally  by  small 

Fig.  302. 


B 


elastic  cord  (better,  small  spiral  wire  coil),  and  connect  the  ball  at  one 
extremity  of  the  series  with  a  suspended  weight  B  (weighing  about 
lk)  ,  and  from  the  ball  at  the  other  extremity  suspend  a  small  weight 
A,  which  may  be  easily  removed  when  desirable.  By  a  simple  vibra- 
tion given  with  the  hand  to  A,  a  wave,  as  CD,  will  be  projected 
through  the  series,  and  on  reaching  B  will  be  reflected  ;  though  when 
reflection  is  wanted,  B  had  better  be  replaced  by  a  hook  attached  to  a 
wall. 


APPENDIX. 


407 


Fig.  303. 


SECTION   H. 

Porte  Lumiere.  —  Two  half-sections  of  a  tube  A  and  B  (Fig.  303) 
may  easily  be  sawn  from  a  block  of  pine  wood.  These  glued  together 
at  their  edges  make  the  tube  C. 
This  tube  is  20cm  long  and  15*™  in 
diameter,  with  a  bore  of  llcm  diam- 
eter. Raise  a  window-sash  about 
50cm,  and  fit  a  board  D  just  to  fill 
the  opening.  In  the  middle  of  this 
board  cut  a  hole  just  large  enough 
to  receive  the  tube,  and  allow  it  to 
turn  in  the  hole  freely.  Attach  a 
bolt  E  to  the  board  D,  and  about 
1 2cm  from  one  end  of  the  tube  bore 
a  row  of  holes  around  the  tube, 
lcm  in  depth  and  about  lctn  apart, 
to  receive  the  bolt.  By  means  of  a 
hinge,  attach  to  the  outer  edge  of  the  tube  a  board  G,  30cm  long,  14cm  wide, 
and  1.5cm  thick.  A  mirrov  F,  26cm  long  and  12cm  wide,  is  fastened  by 
tacks  with  large  heads  to  the  upper  surface  of  this  board.  A  stout 
string  attached  to  one  of  the  long  edges  of  the  board  is  carried  through 
the  tube  and  fastened  to  a  binding  screw  H.  When  the  mirror  is  to 
be  adjusted  so  as  to  receive  the  sun's  rays  and  reflect  them  through  the 
tube,  rotate  the  tube,  and  raise  or  depress  the  mirror  by  means  of  the 
string,  so  as  to  adapt  it  to  the  position  and  elevation  of  the  sun  in  the 
heavens,  and  then  fasten  by  means  of  the  bolt  and*  string.  A  win- 
dow on  the  south  side  of  a  building  should  be  selected  for  experiments 
with  this  apparatus.  The  portion  of  the  window  not  occupied  with 
the  board  D,  as  well  as  other  windows  not  in  use,  may  be  darkened 
with  curtains  of  black  enamelled  cloth.  The  whole  cost  of  the  above 
apparatus  need  not  exceed  $1.00. 


SYLLABUS. 

CHAPTER  I. 

V 

MATTER  AND   ITS   PROPERTIES. 


I.   INTRODUCTION. 

AN  experiment  is  a  question  put  to  Nature. 

By  experiment  we  learn  that  invisible  air,  like  matter,  and 
like  nothing  else  with  which  we  are  acquainted,  can  displace 
matter  (e.g.,  a  bubble),  exert  pressure,  and  has  weight ;  hence, 
we  conclude  that  air  is  matter,  and  that  matter  can  exist  in  an 
invisible  state. 

No  visible  body  of  matter,  however  compact  it  may  appear, 
ever  Jills  the  space  enclosed  by  its  surface ;  but  every  visible 
body  is  a  collection  of  countless  smaller  bodies  called  molecules, 
separated  by  invisible  spaces  called  pores.  Every  molecule  is 
in  motion,  and  this  motion  is  such  as  to  prevent  permanent 
contact  between  one  another. 

By  the  mass  of  a  body  we  understand  the  quantity  of  matter 
in  it ;  and  by  its  density,  the  mass  in  a  unit  volume. 

Substances  whose  molecules  can  be  separated  into  molecules 
differing  in  substance  from  the  original  molecules  are  called 
compound.  Substances  whose  molecules  have  never  been  so 
separated  are  called  simple.  There  are  known  only  about  71 
of  the  latter,  and  an  innumerable  number  of  the  former. 

Any  change  in  a  body  that  does  not  cause  a  change  of  sub- 
stance is  a  physical  change.  A  change  of  substance  is  a  chemi- 
cal change 


410  SYLLABUS. 

Matter  is  nowhere  created,  nowhere  annihilated.  The  mass 
of  the  universe  is  constant. 

The  tendency  which  matter  possesses  to  push  and  to  pull  is 
called  force.  Whatever  tends  to  produce  or  alter  motion  is 
force.  It  is  manifested  only  in  pushes  and  pulls. 

Forces  are  classified  as  molecular  or  molar,  according  as  they 
act  between  molecules  or  larger  bodies ;  attractive  or  repellent, 
according  as  they  are  manifested  in  pulls  or  pushes. 

When,  by  external  force,  the  molecules  of  a  body  are  brought 
nearer  together,  it  is  said  to  be  compressed  or  condensed;  if  they 
are  brought  together  by  internal  forces,  the  body  is  said  to  con- 
tract, and  if  they  are  separated  by  internal  forces,  it  is  said  to 
expand. 

II.  THREE  STATES  OF  MATTER. 

Any  substance  may  exist  in  any  one  of  three  states,  —  solid, 
liquid,  or  gaseous. 

General  characteristics  of  matter  in  the  solid  state  :  Immobil- 
ity of  the  molecules,  and  permanence  of  shape. 

Liquid  state :  Greater  mobility  of  the  molecules,  easily  poured, 
and  shaped  by  the  containing  vessels. 

Gaseous  state :  Almost  perfect  freedom  of  motion  of  the  mole- 
cules ;  unlimited  tendency  to  expand  ;  great  compressibility. 

Owing  to  their  tendency  to  flow,  both  liquids  and  gases  are 
called  fluids. 

•     The  state  which  a  body  assumes  depends  on  temperature  and 
pressure. 

III.  PHENOMENA  OF  ATTRACTION. 

The  force  of  attraction  which  exists  between  all  bodies  at 
distances  however  great  is  called  the  force  of  gravity,  and  the 
phenomenon  is  called  gravitation.  Weight  is  a  term  applied 
to  the  measure  of  this  force  as  exerted  between  the  earth  and 
terrestrial  objects.  Weight  varies  as  the  mass,  and  with  the 
distance  from  the  centre  of  the  earth.  At  the  same  place, 
weight  is  proportional  to  the  mass. 


MATTER  AND  ITS   PROPERTIES.  411 

When  attraction  is  molecular,  and  between  like  molecules,  it 
is  called  cohesion;  when  between  unlike  molecules,  it  is  called 
adhesion. 

When  a  body  of  matter  in  a  solid  state  exhibits  method  in 
the  arrangement  of  its  molecules,  it  is  said  to  be  crystalline; 
otherwise,  amorphous.  Matter  crystallizes,  usually,  while  pass- 
ing from  the  liquid  to  the  s^lid  state. 

A  theory,  suggested  as  a  possible  explanation  of  the  cause  of 
crystallization,  is  based  upon  the  hypothesis  that  the  molecules 
of  crystalline  matter  possess  something  akin  to  polarity,  in  which 
case  the  molecules  would  tend  to  arrange  themselves  somewhat 
as  iron  filings  do  when  they  possess  polarity. 

Hardness  is  due  to  some  peculiar  action  (not  well  understood) 
of  cohesion,  that  enables  a  body  to  resist  another  body  tending 
to  scratch  it. 

When  molecular  forces  tend  to  restore  a  body  to  its  original 
shape  and  volume  after  having  yielded  to  some  force,  they  are 
called  elastic  forces,  and  the  body  is  said  to  possess  the  property 
of  elasticity. 

Substances  which  tend  to  break  rather  than  suffer  a  permanent 
alteration  in  form  are  said  to  be  brittle. 

Substances  which,  though  brittle  when  a  force  is  applied  sud- 
denly, will  suffer  a  permanent  change  in  form  if  subjected  to  a 
gradual  and  long-continued  stress,  are  called  viscous. 

All  substances  in  the  solid  state  possess,  to  some  extent,  the 
property  of  fluidity,  and  hence  are  more  or  less  flexible,  malle- 
able, and  ductile.  This  implies,  also,  that  they  possess  a  power 
of  preventing  rupture  when  subjected  to  a  pulling  force.  This 
power,  due  to  cohesion,  is  called  tenacity. 

Liquids  ascend  or  are  depressed  in  capillary  tubes  according 
as  the  adhesion  between  the  liquid  and  the  tubes  is  greater  or 
less  than  the  cohesion  in  the  liquids.  For  the  four  laics  of 
capillary  action,  see  page  36. 

A  liquid  will  dissolve  a  solid  when  the  adhesion  is  greater 
than  the  cohesion. 


412  SYLLABUS. 

Absorption  of  gases  by  solids  is  caused  chiefly  by  molecular 
attraction,  and  is  said  to  be  superficial  when  the  gases  are 
taken  into  the  cavities  of  solids,  and  intermolecular  when  taken 
into  the  pores. 

Absorption  of  gases  by  liquids  is  intermolecular,  and  is 
caused  both  by  attraction  of  the  molecules  and  their  incessant 
motion. 

Diffusion  of  liquids  is  caused  mainly  by  the  motion  of  their 
molecules. 

Osmose,  or  the  diffusion  of  liquids  through  porous  septa,  is 
imperfectly  understood,  though  it  is  supposed  that  adhesion  be- 
tween the  liquids  and  the  septa  is  the  chief  agent. 

Diffusion  of  gases  depends  almost  wholty  on  molecular  motion. 
All  gases  diffuse  regardless  of  the  force  of  gravity. 

Osmose  depends  on  the  size  of  molecules,  size  of  pores,  and 
on  molecular  motion  ;  very  complex. 


CHAPTER  II. 
DYNAMICS. 

IV.   DYNAMICS   OF  FLUIDS. 

Dynamics  treats  of  force  and  motion.  When  several  forces 
so  act  on  a  body  as  to  neutralize  one  another's  effect,  both  the 
forces  and  the  body  are  said  to  be  in  equilibrium.  A  body  in 
a  state  of  rest  or  uniform  motion  is  in  equilibrium. 

(Can  absolute  rest  or  uniform  motion  exist  except  there 
is  absolute  equilibrium?  Is  there  any  body  known  to  be  in 
a  state  of  absolute  equilibrium,  i.e.,  in  equilibrium  with  refer- 
ence to  all  external  forces  ?) 

When  a  pushing  force  is  resisted,  «.e.,  when  any  portion  of 
the  force  is  not  effective  in  producing  motion,  there  results  a 
pressure.  Under  similar  conditions  a  pulling  force  causes 
tension.  (The  word  tension  is  also  applied  to  the  expansive 
power  of  gases.) 

At  every  point  in  a  body  of  fluid,  gravity  causes  pressure  to 
be  exerted  equally  in  all  directions.  In  gases  the  pressure 
increases  with  the  depth  ;  in  liquids,  as  the  depth. 

The  average  sea-level  atmospheric  pressure  (and  consequently 
the  tension  of  the  air  at  this  level)  is  1033.3g  (about  lk)  per 
square  centimeter,  or  14.7  Ibs.  (about  15  Ibs.)  per  square  inch. 
An  atmosphere  (when  the  term  is  used  to  denote  pressure)  is 
the  pressure  of  lk  per  square  centimeter.  Any  instrument 
which  will  measure  atmospheric  pressure  is  a  barometer. 

MARIOTTE'S  or  BOYLE'S  LAW  :  At  the  same  temperature  the 
volume  of  a  body  of  gas  varies  inversely  as  the  pressure, 
density,  or  elastic  force. 

In  consequence  of  the  mobility  and  perfect  elasticity  of  fluids, 


414  SYLLABUS. 

any  pressure  exerted  on  a  given  area  of  a  fluid  enclosed  in  a 
vessel  is  transmitted  undiminished  to  every  equal  area  of  the 
interior  of  the  vessel.  In  the  hydrostatic  (or  hydraulic)  press 
we  have  a  practical  application  of  this  principle. 

The  pressure  on  the  bottom  or  sides  of  a  vessel,  due  to  the 
gravity  of  the  liquid  which  it  holds,  depends  on  the  depth  and 
urea  of  the  surface  pressed  upon,  and  the  density  of  the  liquid, 
and  is  independent  of  the  shape  of  the  vessel  and  the  quantity 
of  liquid. 

The  pressure  upon  any  portion  of  a  vessel  is  the  weight  of  a 
column  of  that  liquid  whose  base  is  the  area  of  the  portion 
pressed  upon,  and  whose  hight  is  the  average  depth  of  that 
portion. 

The  free  surface  of  a  body  of  liquid,  at  rest,  partakes  of  the 
sphericity  of  the  earth,  but  for  most  practical  purposes  may  be 
regarded  as  level. 

V.  BUOYANT  FORCE  OF  LIQUIDS. 

A  solid  immersed  in  a  fluid  is  buo}'ed  up  by  it  in  consequence 
of  the  unequal  pressures  upon  the  top  and  bottom  at  their  dif- 
ferent depths,  and  the  amount  of  buoj'anc}'  (or  the  apparent 
loss  of  weight  of  the  solid)  is  the  weight  of  a  body  of  that  fluid 
whose  volume  is  equal  to  the  volume  of  the  solid.  A  floating 
solid  displaces  its  own  weight  of  fluid.  The  absolute  weight  of 
a  body  is  its  weight  in  a  vacuum. 

VI.   DENSITY  AND   SPECIFIC  GRAVITY. 

The  specific  gravity  of  a  substance  is  the  ratio  of  the  density 
of  that  substance  to  the  density  of  another  substance  taken  as 
a  standard.  It  is  found  by  dividing  the  weight  of  a  given 
volume  of  the  substance  by  the  weight  of  an  equal  volume  of 
the  standard.  (In  finding  the  specific  gravity  of  solids  and 
liquids,  state  various  methods  of  ascertaining  the  weight  of  an 
equal  volume  of  the  standard.) 


DYNAMICS.  416 


VII.    MOTION. 

Motion  and  rest  are  wholly  relative  terms,  i.e.,  they  are 
applicable  to  an  object  only  when  considered  in  connection  with 
some  other  object.  There  is  no  such  thing  as  absolute  rest  in 
the  universe. 

Velocity  is  given  in  units  of  space  and  time. 

Motion  is  uniform  or  varied.  Varied  motion  is  accelerated 
or  retarded.  We  may  conceive  of  uniform  motion  though  it 
nowhere  exists. 

VIII.     FIRST   LAW  OF   MOTION.  —  INERTIA. 

Motion  always  arises  from  mutual  action  between  at  least 
two  bodies,  and  cannot  originate  in  an  object  isolated  from  all 
others. 

Motion  in  a  body  is  caused  only  by  another  body's  parting 
with  some  of  its  power  of  producing  motion. 

Bodies  receive  motion  gradually  and  part  with  it  gradually. 

No  body  possesses  any  innate  power  to  change  its  condition 
with  reference  to  motion  or  rest.  It  is  sometimes  convenient  to 
speak  of  this  complete  absence  of  power  as  a  property  of  matter, 
under  the  name  of  inertia. 

First  Law  of  Motion.  — A  bod}r  at  rest  remains  at  rest 
(why?),  and  a  bod}'  in  motion  moves  with  uniform  velocity 
(why?)  in  a  straight  line  (why?),  unless  acted  upon  by  some 
external  force  to  change  its  condition. 

IX.     SECOND   LAW   OF   MOTION,   AND  APPLICATIONS. 

Second  Law  of  Motion.  —  A  given  force  has  the  same  effect 
in  producing  motion,  whether  the  body  on  which  it  acts  is  in 
motion  or  at  rest ;  whether  it  is  acted  upon  by  that  force  alone, 
or  by  others  at  the  same  time. 

It  is  usually  possible  to  substitute  for  two  or  more  forces  a 


416  SYLLABUS. 

single  force  which  will  produce  the  same  result  as  the  combined 
forces.     Such  a  force  is  called  a  resultant. 

The  resultant  of  two  forces  acting  at  an  angle  to  each  other 
may  be  represented  by  a  diagonal  of  a  parallelogram,  of  which 
the  components  form  two  adjacent  sides. 

Any  single  force  may  be  resolved  into  two  or  more  compo 
nents. 

The  resultant  of  parallel  forces  having  the  same  direction  is 
their  sum  ;  the  resultant  of  two  parallel  forces  acting  in  opposite 
directions  is  motion  in  the  direction  of  the  greater  force  propor- 
tionate to  their  difference. 

When  two  parallel  forces  having  the  same  direction  act  upon 
a  body  at  different  points,  the  distances  of  their  points  of 
application  from  the  points  of  application  of  their  resultant  are 
inversely  as  their  intensities. 

A  pair  of  forces,  equal,  parallel,  opposite,  and  applied  at 
opposite  extremities  of  an  object,  produces  only  rotation,  and  is 
called  a  couple.  A  couple  has  no  resultant  and  no  equilibrant. 

X.    CENTER   OF   GRAVITY. 

The  center  of  gravity  of  a  body  is  the  point  of  application  of 
the  resultant  of  the  forces  of  gravity  acting  on  its  molecules. 
To  support  any  body,  it  is  only  necessary  to  provide  an  equi- 
librant for  this  resultant,  and  to  apply  it  at  some  point  in  the 
line  of  direction.  Whether  a  body  will  stand  or  fall  depends 
upon  whether  its  line  of  direction  falls  within  its  base,  i.e., 
whether  its  support  is  applied  in  the  line  of  direction. 

A  body  tends  to  assume  a  position  such  that  its  e.g.  will  be 
as  low  as  possible,  and  when  in  such  position  it  is  said  to  be  in 
stable  equilibrium.  When  a  disturbance  would  lower  its  e.g.,  it 
is  said  to  be  in  unstable  equilibrium;  and  when  disturbance 
would  not  lower  or  raise  its  e.g.,  it  is  in  neutral  equilibrium. 
A  broad  base  and  low  e.g.  give  stability  to  a  body. 


DYNAMICS.  417 

XI.     CURVILINEAR  MOTION. 

A  curved  line  is  one  whose  direction  changes  at  every  point. 
To  produce  curvilinear  motion,  a  continuous  (why  continuous?) 
force  must  be  applied  at  an  angle  (why?)  to  its  otherwise 
straight  path.  (See  First  Law  of  Motion.)  Centrifugal  force 
is  the  result  of  the  tendency  of  a  body  to  move  in  a  straight 
line ;  centripetal  force  is  tjie  force  which  compels  it  to  depart 
from  a  straight  line. 

Centrifugal  force  increases  as  the  mass  and  the  square  of  the 
velocity ;  hence,  to  produce  circular  motion,  the  centripetal 
force  must  increase  as  the  mass  and  the  square  of  the  velocity. 

XII.     ACCELERATED   AND  RETARDED  MOTION. 

A  body  impelled  by  a  single  constant  force,  and  encounter- 
ing no  resistance,  always  has  a  uniformly  accelerated  motion. 
A  moving  body,  encountering  constant  resistances,  has  uni- 
formly retarded  motion.  The  acceleration  or  retardation  per 
unit  of  time  is  represented  by  k  (or  g,  when  the  force  is  gravity). 

Formulas  for  uniformly  accelerated  motion:  — 

(1)  V  =  (ifcx2T)  =  &T 

(2)  a  =  ifc(2T-l) 

(3)  S  =  i&T2 

Hence,  velocity  varies  as  the  time,  and  the  entire  distance  trav- 
ersed as  the  square  of  the  time. 

The  acceleration  due  to  gravity  in  the  Northern  States,  near 
the  sea  level,  when  there  are  no  resistances,  is  (g)  9.8m(or32.2 
ft.)  per  second.  This  is  the  measure  of  the  force  of  gravity  at 
these  places. 

All  bodies,  of  whatever  mass,  density,  or  substance,  fall  with 
equal  velocities  in  a  vacuum.  (Why?) 

The  horizontal  distance  attained  by  a  projectile  is  its  range  or 
random.  The  greatest  range  is  obtained  at  an  angle  a  little 
less  than  40°. 


418  SYLLABUS. 

A  body  projected  horizontally,  with  any  velocity,  will  reach 
the  ground  in  precisely  the  same  time  that  it  would  if  dropped 
vertically.  (Why?) 

xiii.   THE  PP:NDULUM. 

The  time  of  vibration  of  a  pendulum  varies  inversely  as  the 
number  of  vibrations. 

The  time  of  vibration  and  the  number  of  vibrations  are  inde- 
pendent of  both  the  mass  and  the  length  of  arc. 

The  time  of  vibration  and  the  number  of  vibrations  depend 
upon  both  the  length  of  the  pendulum  and  the  force  of  gravity. 

The  time  of  vibration  varies  as  the  square  root  of  the  length 
of  the  pendulum. 

The  number  of  vibrations  varies  inversely  as  the  square  root 
of  the  length  of  the  pendulum. 

The  time  of  vibration  varies  inversely  as  the  square  root  of 
the  force  of  gravity. 

The  number  of  vibrations  varies  as  the  square  root  of  the 
force  of  gravity. 

The  length  of  a  pendulum  is  the  distance  from  the  point 
of  suspension  to  its  center  of  oscillation.  These  two  points  are 
interchangeable . 

The  center  of  percussion  is  coincident  with  the  center  of 
oscillation. 

XIV.    MOMENTUM.— THIRD  LAW  OF  MOTION. 

Momentum  is  the  product  of  mass,  multiplied  by  velocity ;  or, 
it  is  the  product  of  force,  multiplied  by  the  time  during  which  it 
acts. 

Third  Law  of  Motion.  To  every  action  there  is  an  equal  and 
opposite  reaction. 

The  momentum  of  the  reaction  is  equal  to  the  momentum  of 
the  action. 

Law  of  Reflection. — When  the  striking  body  and  the  body 
struck  are  perfectly  elastic,  the  angle  of  reflection  is  equal  to 
the  angle  of  incidence. 


DYNAMICS.  419 

XV.   WORK.—  ^NERGY. 

Work  is  done  whenever  force  acts  through  space.  It  is 
estimated  by  multiplying  resistance  by  the  space,  or  force  by  the 
space  through  which  it  acts.  It  is  commonly  expressed  in  kilo- 
grammeters  or  foot  pounds. 

In  estimating  the  rate  of  doing  work,  or  the  power  of  an 
agent  to  do  work,  time  is  taken  into  consideration.  The  unit 
employed  is  a  horse-power,  which  is  a  power  capable  of  doing 
33,000  ft.  Ibs.  =  4,570kgm  per  minute. 

Power  to  do  work  is  called  energy.  Every  moving  body 
possesses  energy  due  to  its  motion;  energy  due  to  motion  is 
called  kinetic  energy.  A  body  may  possess  energy  due  to  an 
advantage  of  position  given  it  by  work  done  upon  it.  Energy 
due  to  position  is  called  potential.  Potential  energy  becomes 
kinetic  on  the  return  of  bodies  to  their  original  positions. 

Formulas  for  energy  : 

wv2 
(1)  Energy  =          J 


(2)  Energy  = 
But,  since  W=M#, 


g 

hence,  in  using  the  second  formula,  the  value  of  M  must  be  found 
by  dividing  W  by  g. 

Force  may  be  measured  by  the  change  of  momentum  it  pro- 
duces in  a  second. 

In  the  C.G.S.  system,  the  centimeter,  gram,  and  second  are 
taken  as  the  units  of  distance,  mass,  and  time  respectively,  and 
in  it  the  dyne  is  the  unit  of  force.  A  dyne  is  a  force  which, 
acting  for  a  second,  will  give  to  a  gram  of  matter  a  velocity  of 
one  centimeter  per  second. 


420  SYLLABUS. 

In  the  gravitation  system  the  term  gram  (or  pound,  etc.)  is 
applied  to  both  mass  and  force. 

In  the  C.G.S.  system  the  unit  of  work  is  the  erg.  The  erg 
and  kilogrammeter  measure  both  work  and  energy,  or  power  to 
do  work.  An  erg  is  the  work  done,  or  the  energy  imparted,  by 
a  force  of  one  dyne  working  through  a  distance  of  one  centi- 
meter. 

Energy  may  be  transformed  from  one  condition  to  another,  as 
from  kinetic  to  potential ;  or,  from  one  variety  to  another,  as 
from  heat  to  mechanical  or  molar  motion. 

Physics  treats  of  transferences  and  transformations  of  energy. 

XVI.  MACHINES. 

Advantages  of  machines:  (1)  They  enable  us  to  exchange 
power  for  velocity,  or  velocity  for  power.  (2)  They  enable  us 
to  employ  a  force  in  a  direction  which  is  more  convenient  than 
the  direction  in  which  the  resistance  is  to  be  moved.  (3)  They 
enable  us  to  employ  other  forces  than  our  own  in  doing  work. 

LAW  OF  MACHINES  :  The  work  applied  to  a  machine  is  equal 
to  the  effective  work  plus  the  internal  work  done  by  the  machine. 
The  useful  work  done  by  a  machine  is  less  than  the  work  done 
upon  the  machine.  In  a  perfect  machine  they  would  be  equal. 
None  exists. 

In  every  machine  P :  W  ::  W  :p  ;  ?'.e.,  The  power  and  resist- 
ance vary  inversely  as  the  distances  they  respectively  travel- 


CHAPTER  III. 

MOLECULAR  ENERGY. -HEAT. 
XVII.    WHAT  HEAT  IS.  — SOME  SOURCES  OF  HEAT. 

Two  theories  of  heat  have  successively  prevailed,  viz. :  (1) 
that  heat  is  matter;  (2)  that  it  is  motion.  Molar  motion  is 
convertible  into  heat,  and  heat  is  convertible  into  molar  motion. 
It  is  scarcely  conceivable  that  motion  can  be  converted  into 
matter,  or  matter  into  motion.  But  it  is  a  matter  of  everyday 
observation,  that  when  motion  of  one  kind  (or  thing)  ceases, 
motion  of  another  kind  (or  thing)  takes  its  place.  Conclusion  : 
heat  is  motion,  i.e.,  molecular  motion  ;  this  implies  the  existence 
of  kinetic  energy. 

Molecules  may  possess  potential  energy,  which  becomes  kinetic 
during  chemical  action,  i.e.,  the  clashing  together  of  molecules 
in  consequence  of  affinity,  thereby  generating  heat,  as  in  com- 
bustion. This  is  the  origin  of  animal  heat  and  muscular  motion. 
The  sun  is  the  ultimate  source  of  nearly  all  the  energy  at  man's 
command. 

Temperature  is  determined  by  the  average  kinetic  energy  of 
the  individual  molecule ;  quantity  of  heat,  by  the  average 
kinetic  energy  of  the  individual  molecule  multiplied  by  the 
number  of  molecules. 

XIX.   DIFFUSION   OF   HEAT. 

Heat  is  diffused  by  conduction,  convection,  and  radiation. 
(Explain  the  first  two.  How  is  ventilation  usually  accomplished  ? 
By  which  method  do  we  receive  heat  from  the  sun?  Why  not 
by  either  one  of  the  other  two  methods  ?) 


422  SYLLABUS. 

XX.   EFFECTS   OF   HEAT.  —  EXPANSION. 

Effects  of  heat :  Expansion,  liquefaction,  vaporization,  change 
of  temperature,  and  specific  heat  in  part. 

(In  what  state  is  matter  least  expansive ?  Why?  In  what 
state  is  the  coefficient  of  expansion  the  same  for  all  substances  ? 
What  is  the  coefficient?  State  an  exception  to  the  general  rule 
that  matter  expands  with  a  rise  of  temperature.) 

XXI.  THERMOMETRY. 

Change  of  temperature  is  measured  by  expansion.  A  ther- 
mometer measures  expansion,  hence  it  measures  temperature. 

(State  the  method  of  construction  and  graduation  of  a  mercury 
thermometer.  What  kind  of  thermometer  is  more  sensitive 
than  a  mercury  thermometer?  Wh}T?) 

Formulas  for  conversion  of  thermometer  readings  : 

|  (F-32)  =C;  f  C  +  32  =  F. 

Absolute  temperature  is  reckoned  from  an  absolute  zero,  or 
state  of  no  heat.  It  may  be  found  by  adding  273  to  the  C. 
reading,  or  460  to  the  F.  reading. 

LAW  OF  CHARLES  :  The  volume  of  a  given  body  of  gas  at  a 
constant  pressure  varies  as  its  absolute  temperature. 

Conversely,  the  tension  of  a  given  body  of  gas,  whose  volume 
is  constant,  varies  as  its  absolute  temperature. 

MARIOTTE'S  LAW  :  At  a  constant  temperature,  the  volume  of  a 
given  body  of  gas  varies  inversely  as  the  external  pressure.  At 
a  constant  temperature,  the  product  of  the  volume  and  tension 
of  a  given  body  of  gas  is  constant.  The  product  of  the  volume 
and  tension  of  a  body  of  gas  varies  as  its  absolute  temperature. 

The  tension  of  a  bod}'  of  gas  is  due  to  the  kinetic  energy  of 
irs  molecuies. 


MOLECULAR   ENERGY.  —  HEAT.  423 

XXII.    LIQUEFACTION  AND   VAPORIZATION. 

See  laws  of  fusion  and  boiling,  page  161. 

Distillation,  or  the  separation  of  mixed  liquids  by  vaporiza- 
tion, is  conducted  on  the  principle  that  the  temperature  of  the 
boiling  points  of  different  substances  differs. 

The  rapidity  of  evaporation  varies  with  the  temperature 
(why?),  amount  of  surface  exposed,  and  dryness  of  the  atmos- 
phere, and  inversely  with  the  pressure  upon  the  liquid.  Dew- 
point  is  the  temperature  of  the  atmosphere  when  saturated  with 
watery  vapor.  The  atmosphere  is  dry  when  the  difference 
between  its  temperature  and  dewpoint  is  great.  The  term  dry- 
ness,  when  applied  to  the  atmosphere,  signifies  capacity  for 
receiving  more  moisture,  and  does  not  necessarily  imply  defi- 
ciency of  moisture. 

[The  molecules  of  every  body  of  liquid  are  in  motion.  The 
distances  traversed  by  the  molecules  in  the  interior  of  a 
body  are  limited  by  the  proximity  of  neighboring  molecules  on 
all  sides.  When  the}T  reach  the  free  surface  of  the  body,  they 
are  not  subject  to  this  restraint,  and  more  or  less  of  them 
depending  upon  the  temperature  (i.e.,  the  energy  of  their  move- 
ments) ,  become  released  from  the  force  of  cohesion  and  pass 
off  as  a  vapor.  This  is  evaporation.  On  the  other  hand,  mole- 
cules of  the  vapor,  resting  upon  the  liquid  surface,  beat  against 
it,  and,  it  is  supposed,  become  entangled  in  it  and  thus  return 
to  the  liquid  state.  When  the  number  of  molecules  which  thus 
return  to  the  liquid  state  equals  those  which  escape,  the  space 
above  the  liquid  is  said  to  be  saturated.] 

XXIII.     HEAT  CONVERTIBLE   INTO   POTENTIAL  ENERGY, 
AND  VICE   VERSA. 

Heat  is  measured  in  calories ;  temperature,  in  degrees.  A 
calorie  is  the  quantity  of  heat  required  to  raise  the  temperature 
of  lk  of  water  from  0°  to  1°  C. 


424  SYLLABUS. 

Eighty  calories  are  consumed  in  converting  one  kilogram  of 
ice  into  water.  Five  hundred  and  thirty-seven  calories  are  con- 
sumed in  converting  lk  of  water  at  100°  C.  into  steam.  In  the 
first  case,  the  heat  is  consumed  in  doing  interior  work,  such  as 
neutralizing,  in  part,  the  force  of  cohesion.  In  the  second 
case,  the  larger  portion  (about  Tf )  of  the  heat  is  consumed  in 
the  interior  work  of  completely  overcoming  cohesion,  and  the 
remaining  portion  (T^)  in  the  exterior  work  of  overcoming 
atmospheric  pressure. 

The  temperature  of  a  body  is  reduced,  either  by  imparting 
heat  to  a  colder  body,  or  by  the  consumption  of  its  heat  in  doing 
work.  By  the  latter  method  artificial  cold  is  produced.  The 
work  done  is  usually  that  of  melting  or  dissolving  some  solid, 
vaporizing  a  solid  or  liquid,  or  producing  expansion  in  a  gas 
against  resistance.  (Give  illustrations  of  each.) 

Heat  which  is  consumed  in  melting,  dissolving,  and  vaporiz- 
ing, is  restored  when  the  opposite  changes  occur.  (Explain.) 

XXIV.     SPECIFIC  HEAT. 

Equal  quantities  of  heat  applied  to  equal  weights  of  different 
substances  raise  their  temperatures  unequally.  In  the  case  of 
solids  and  liquids,  this  is  explained  by  the  fact  that  a  portion  of 
the  heat  applied  is  always  consumed  in  doing  internal  work  ;  and 
since  in  different  substances  the  amount  consumed  in  doing 
work  varies,  consequently  the  amount  of  heat  left  to  raise  the 
temperature  of  different  substances  must  vary. 

The  number  of  heat  units  required  to  raise  a  body  1°  C.  is 
called  its  capacity  for  heat. 

The  specific  heat  of  a  body  is  the  ratio  of  its  capacity  for  heat 
to  that  of  an  equal  weight  of  water. 

Hydrogen  gas  has  the  greatest  capacity  for  heat.  Water  ranks 
next. 


MOLECULAR   ENERGY.  —  HEAT.  425 


XXV.    THERMO-DYNAMICS. 

A  definite  quantity  of  mechanical  work  can  produce  a  defi- 
nite quantity  of  heat ;  and  conversely,  this  heat  can  perform 
the  original  amount  of  work.  One  calorie  is  equivalent  to 
424kgm  of  work.  The  quantity,  424kgm,  is  called  the  mechanical 
equivalent  of  heat. 

Doctrine  of  correlation  of  energy :  Any  kind  of  energy  can  be 
converted  into  any  other  kind. 

Doctrine  of  conservation  of  energy :  When  one  form  or  kind 
of  energy  disappears,  an  exact  equivalent  of  another  form  or 
kind  always  takes  its  place,  so  that  the  sum  total  of  energy  in 
the  universe  is  constant. 

XXVI.     STEAM  ENGINE. 

A  steam  engine  is  a  machine  b}'  means  of  which  a  portion  of 
the  motion  of  the  molecules  of  steam  (i.e.,  its  heat)  is  trans- 
formed into  molar  or  mechanical  motion. 

In  a  non-condensing  engine,  a  large  amount  of  energy  is 
wasted  in  producing  motion  against  the  resistance  of  atmos- 
pheric pressure. 


CHAPTER   IV. 
ELECTRICITY. 

XXVII.     CURRENT  ELECTRICITY. 

Just  as  a  difference  of  level  is  necessary  to  produce  a  current 
of  water,  and  a  difference  of  temperature  to  cause  a  flow  of  heat, 
so  a  difference  of  electrical  condition,  called  a  difference  of 
potential,  is  necessary  to  cause  a  flow  of  electricity.  To  estab- 
lish the  necessary  conditions  in  each  case  (i.e.,  difference  of 
level,  etc.)  energy  must  be  expended.  On  the  other  hand,  the 
return  of  each  to  its  normal  condition  or  state  of  equilibrium  is 
attended  with  the  development  of  energy.  The  constant  expen- 
diture of  chemical  potential  energy  in  a  voltaic  cell  causes  a 
constant  inequality  of  potential,  and  this  in  turn  causes  a  con- 
stant tendency  to  equalization  of  potential  throughout  the  circuit; 
in  other  words,  a  continuous  current. 

As  the  stress  (called  force  of  gravity)  between  an  elevated 
body  of  water  and  the  earth  is  the  cause  of  the  so-called  water- 
power,  so  it  is  probable  that  a  stress  between  two  parts  of  a 
body  having  different  potential  is  the  cause  of  a  power  usually 
called  electro-motive  force. 

The  greater  the  disparity  between  the  two  solid  elements  of 
a  voltaic  cell  with  reference  to  the  action  of  the  liquid  on  them, 
the  greater  the  difference  of  potential  or  electro-motive  force 
of  the  cell ;  hence,  the  stronger  the  current. 

The  office  of  a  voltaic  battery  is  to  create  inequality  of  poten- 
tial, i.e.,  to  generate  electro-motive  force. 

The  zinc  element  generally  needs  to  be  amalgamated  to  pre- 
vent local  action  and  consequent!}'  a  waste  of  energy. 

Hydrogen  ought  not  to  be  allowed  to  collect  on  the  electro- 
negative plate,  as  it  offers  a  resistance  to  the  current,  but 
chiefly  because  it  tends  to  reduce  the  difference  of  potential 


ELECTRICITY.  427 

between  the  two  plates,  and  thereby  reduce  the  current.     This 
may  be  prevented  by  either  mechanical  or  chemical  action. 

The  effects  of  electricity  are  heating,  luminous,  electrolytic, 
physiological,  and  magnetic. 

XXX.  ELECTRICAL  MEASUREMENTS. 

Upon  the  strength  of  the  current  depends  the  magnitude  of 
these  effects.  By  the  strength  of  the  current  is  meant  the 
quantity  of  electricity  which  flows  through  a  circuit  in  a  unit  of 
time.  The  voltameter  and  galvanometer  measure  the  strength 
of  the  current.  In  the  tangent  galvanometer  the  strength  of 
current  is  proportional  to  the  tangent  of  the  angle  of  deflection. 

OHM'S  LAW  :  The  strength  of  the  current  varies  as  the  electro- 
motive force,  and  inversely  as  the  resistance  in  the  entire  circuit; 
i.e.,  an  effect  is  directly  proportional  to  that  which  tends  to  pro- 
duce it,  and  inversely  proportional  to  that  ivhich  tends  to  oppose  it. 

Resistance  varies  as  the  length,  and  inversely  as  the  squares 
of  the  diameters  of  cylindrical  conductors. 

When  the  external  resistance  is  much  greater  than  the 
internal,  it  is  best  to  connect  cells  "tandem"  in  order  to 
increase  the  electro-motive  force.  When  the  internal  resistance 
is  greater  than  the  external,  the  cells  should  be  connected 
k-  abreast"  in  order  to  diminish  the  internal  resistance.  When 
the  external  and  internal  resistances  are  nearly  equal,  it  may  be 
best  to  connect  them  in  both  ways. 

In  a  circuit  having  a  given  external  resistance  the  greatest 
possible  efficiency  is  obtained  from  a  given  battery  when  the  ex- 
ternal and  internal  resistances  are  about  equal. 

XXXI.  MAGNETS   AND   MAGNETISM. 

LAW  OF  MAGNETS  :  Like  poles  repel,  unlike  poles  attract  one 
another. 

THE  LAWS  OF  CURRENTS  on  which  Ampere's  theory  of  magnets 
is  based  are  as  follows :  Parallel  currents  in  the  same  direction 


428  SYLLABUS. 

attract  one  another ;  parallel  currents  in  opposite  directions 
repel  one  another.  Angular  currents  tend  to  become  parallel 
and  flow  in  the  same  direction. 

Ampere's  theory  assumes  that  there  are  constant  currents 
circulating  around  the  molecules  of  every  magnetizable  sub- 
stance, and  that  the  resultant  of  these  forces  in  a  magnet  is  the 
same  as  though  "a  sheet  of  currents"  circulated  around  the 
magnet  as  a  whole.  The  deflection  of  the  magnetic  needle  is 
due  to  the  tendency  of  angular  currents  to  become  parallel. 

The  attractions  or  repulsions  of  the  poles  of  magnets  are  due 
to  the  attractions  or  repulsions  of  parallel  currents  according  as 
they  flow  in  the  same  or  opposite  directions. 

The  earth's  magnetism  is  probably  due  to  the  circulation  of 
currents  around  the  earth,  from  east  to  west,  in  planes  at  right 
angles  to  its  axis.  Substances  which  are  attracted  by  a  magnet 
are  called  paramagnetic;  those  which  are  repelled  are  called 
diamagnetic. 

XXXII.   MAGNETO- ELECTRIC  AND  CURRENT  INDUCTION. 

When  Amperian  currents  (i.e.,  a  magnet)  or  a  battery  cur- 
rent approaches  a  neighboring  closed  circuit,  a  momentary 
current  is  induced  in  this  circuit  opposite  in  direction  to  the 
inducing  current ;  when  carried  away,  a  current  is  induced  in 
the  same  direction  as  the  primary  or  inducing  current.  The 
same  happens  whenever  in  one  of  two  neighboring  circuits  a 
current  is  started  or  stopped  by  making  or  breaking  the  circuit. 
At  these  instants  not  only  are  secondary  or  induced  currents 
sent  through  the  neighboring  circuit,  but,  likewise,  corresponding 
currents  are  induced  in  its  own  circuit.  The  latter  are  called 
extra  currents. 

Briefly,  any  magnetic  or  electrical  disturbance  in  the  neighbor- 
hood of  a  circuit  ivill  induce  currents  in  that  circuit. 

The  currents  established  by  magneto  and  dynamo  machines 
are  induced  currents.  Induced  currents  have  high  tension,  i.e., 
great  power  of  overcoming  resistances. 


ELECTRICITY.  429 

XXXIII.   THERMO-ELECTRICITY. 

When  two  different  metals  so  connected  as  to  form  a  circuit 
are  brought  in  contact,  and  heated  or  cooled  at  the  junction,  a 
thermo-electric  current  is  established. 

The  electro-motive  force,  and  consequently  the  strength  of  the 
current,  depends  upon  the  elevation  or  depression  of  tempera- 
ture at  their  junction,  and  upon  the  metals  employed. 

XXXIV.  ERICTIONAL  ELECTRICITY. 

Friction  between  two  bodies,  especially  if  they  are  composed 
of  unlike  substances,  tends  to  produce  a  difference  of  potential 
in  the  bodies.  As  long  as  the  bodies  remain  in  this  condition 
they  are  said  to  be  electrified  or  charged  with  electricity ;  one 
with  positive,  the  other  with  negative  electricity.  Electricity  in 
this  condition  is  said  to  be  static.  On  the  return  of  either  to 
its  normal  potential  a  discharge  is  said  to  occur,  a  current  is 
established,  and  the  electricity  for  the  time  being  is  said  to  be 
dynamic.  As  commonly  understood,  an  electrified  body  is  one 
that  has  a  different  potential  from  that  of  the  earth,  and  is  said 
to  be  positively  electrified  when  its  potential  is  higher  than  that 
of  the  earth,  and  negatively  electrified  when  lower  than  that  of 
the  earth.  Similarly-electrified  bodies  repel  one  another ;  dis- 
similarty-electrified  bodies  attract  one  another.  [Phenomena 
of  electric  attraction  and  repulsion  are  thought  by  many  to  be 
phenomena  of  ether-stress,  or  of  "action  at  a  distance"  through 
the  medium  of  ether.] 

An  electrified  body  brought  near  a  body  whose  potential  is 
zero  tends  to  electrify  it  by  induction,  causing  the  part  of  the 
body  nearest  itself  to  be  of  a  different  potential  from  itself, 
while  the  remote  part  of  the  body,  if  it  is  insulated,  becomes  of 
like  potential.  The  electricity  in  the  former  case  is  said  to  be 
bound,  while  the  latter  is  free,  since,  if  the  insulated  body  is 
connected  with  the  earth,  a  discharge  of  the  latter  occurs ;  in 


430  SYLLABUS. 

other  words,  the  location  of  this  potential  is  transferred  to  the 
earth. 

Electrification  is  confined  to  the  surface  of  a  body. 

XXXV.     ELECTRICAL   MACHINES. 

By  means  of  the  so-called  electrical  machines  mechanical 
energy  is  transformed  into  electric  energy.  These  machines 
are  capable  of  producing  a  great  change  in  potential,  con- 
sequently their  electro-motive  force  is  great,  but  their  internal 
resistance  is  so  great  that  the  strength  of  current  they  are 
capable  of  yielding  is  extremely  small,  and  consequently  they 
are  of  little  practical  value. 

The  phenomena  of  electricity  in  a  statical  state  are  limited  to 
those  of  attraction  and  repulsion.  All  other  effects  are  produced 
by  electricity  in  the  dynamical  state,  and  the  magnitude  of  the 
effects  generally  varies  as  the  square  of  the  current. 

No  one  knows  what  electricity  is.  [It  is  not  ua  form  of 
energy."]  For  practical  purposes,  it  suffices  to  regard  it  as  a 
medium  for  communication  of  energy,  and  to  know  the  laws  to 
which  it  is  subject. 

XXXVI.    USEFUL  APPLICATIONS  OF  ELECTRICITY. 

These  are  well-nigh  innumerable.  Some  of  the  more  impor- 
tant are  those  pertaining  to  medical  and  surgical  operations, 
electric  lighting,  electrotyping,  electroplating,  telegraphy,  tele- 
phony, and  the  production  of  mechanical  motion  through  the 
instrumentality  of  electro-motors  in  great  variety.  [One  of  the 
most  recent  applications  is  that  of  storing  energy,  as  in  the  so- 
called  storage-batteries.  Energy  of  any  kind,  e.g.  water-power 
of  any  of  the  great  water-falls,  may  be  transformed  into  electric 
energy,  and  the  latter  may  be  transformed  into  potential  energy 
and  stored  in  these  batteries.  These  batteries  may  be  trans- 
ported to  distant  places,  and  the  potential  energy  restored  to 
electric  energy,  and  made  to  do  any  species  of  work.] 


CHAPTER   V. 
SOUND. 

XXXVIII.     VIBRATION   AND    WAVES. 

A  vibration  is  a  recurrent  change  of  position.  The  propaga- 
tion of  a  vibration  through  a  series  of  particles  produces  wave 
motion.  A  succession  of  such  propagations  produces  a  wave- 
line.  Only  the  wave-form  advances.  The  distance  between 
any  point  on  one  wave  and  a  similarly  situated  point  on  its 
successor  or  predecessor  is  a  wave-length.  The  greatest  dis- 
tance which  a  particle  reaches  from  its  median  position  is  the 
amplitude  of  the  vibration  or  wave.  The  distance  traversed 
by  a  given  wave  in  one  second  is  the  velocity  of  propagation. 
If  v  be  the  velocit}',  I  the  wave-length,  and  n  the  number  of 
waves  per  second, 

V  ,     7  V 

v  =  nL  n  =  -,  and  I  =  -. 
I  n 

When  a  given  particle  is  subjected  simultaneously  to  two  or 
more  impulses,  due  to  two  or  more  trains  of  waves,  the  motion 
of  the  particle  is  the  resultant  of  the  several  impulses,  and  the 
phenomenon  is  called  interference.  Interference  may  intensify 
or  nullify  motion.  In  cords,  membranes,  etc.,  it  may  result  in 
vibration  in  segments,  or  stationar}T  vibrations,  the  points  of 
least  vibration  being  called  nodes,  the  points  of  greatest  motion, 
antinodes,  and  the  portion  between  two  nodes,  a  ventral  seg- 
ment or  loop. 

Waves  are  longitudinal  or  transverse,  according  as  the  par- 
ticles vibrate  in  the  same  plane  with  the  path  of  the  wave,  or 
across  it. 

Wuve  motion  is  one  of  the  most  common  and  most  important 


432  SYLLABUS. 

methods  of  transmission  of  energy.  Elasticity  is  essential  in  a 
medium,  that  it  may  transmit  waves  made  up  of  condensations 
and  rarefactions  ;  and  the  greater  the  elasticity,  the  greater  the 
facility  and  the  rapidity  with  which  a  medium  transmits  waves. 

XXXIX.     SOUND-WAVES. 

Sound  is  vibration  that  ma}'  be  appreciated  by  the  ear,  and 
originates  in  a  vibrating  body.  It  is  transmitted  by  wave 
motion,  and  therefore  cannot  travel  in  a  vacuum. 

XL.     VELOCITY   OF   SOUND. 

The  velocity  of  sound  in  gases  varies  as  the  square  root 
of  their  elasticity,  and  inversely  as  the  square  root  of  their 
densities. 

XLI.     REFLECTION  AND   REFRACTION   OF  SOUND. 

Sound-waves  are  reflected  in  accordance  with  the  general  law 
of  reflection.  Echoes  are  the  result  of  reflected  sound-waves. 

When  the  form  or  direction  of  a  wave  is  altered  in  consequence 
of  changing  media  of  different  densities  the  phenomenon  is  called 
refraction. 

XLII.     LOUDNESS  OF  SOUND. 

Loudness,  which  is  a  measure  of  the  intensity  of  a  sensation, 
varies  with  the  intensity  of  sound,  but  there  are  many  reasons 
why  they  are  not  exactly  proportional. 

The  intensity  of  sound  varies  as  the  square  of  the  ampli- 
tude of  the  vibrations  of  the  sounding  body.  It  is  also  affected 
by  the  density  of  the  medium  in  which  it  is  produced,  being 
weaker  when  originating  in  a  rare  medium.  The  intensity  of 
sound  varies  inversely  as  the  square  of  the  distance  from  the 
source.  When  sound  is  re-enforced  or  intensified  by  interfer- 
ence the  phenomenon  is  called  resonance.  Re-enforcement  is 
produced  by  means  of  sounding-boards,  columns  of  air,  etc. 


SOUND.  433 

When  one  vibrating  body  causes  another  body  having  the 
same  vibration  period  to  vibrate,  the  vibrations  of  the  latter  are 
called  sympathetic  vibrations.  They  represent  the  accumulated 
effect  of  a  series  of  impulses  transmitted  from  the  sounding  body 
through  the  sound  medium  to  the  body  thus  caused  to  vibrate. 

When  a  vibratile  body  is  compelled  to  surrender  its  own 
vibration  period  and  to  vibrate  in  an  arbitrary  manner  imposed 
upon  it  by  another,  the  phenomenon  is  known  as  forced  vibra- 
tions. 

The  sensation  of  noise  is  caused  by  irregularity  in  the  im- 
pulses received  by  the  ear  and  by  its  inability  to  distinguish 
pitch.  Regularity  and  simplicity  are  characteristics  of  musical 
sound. 

XLIIL    PITCH  OF  SOUND. 

Pitch  depends  upon  vibration-frequency  or  wave-length ;  the 
greater  the  number  of  vibrations  per  second,  or  the  shorter  the 
wave-length,  the  higher  the  pitch.  The  siren  is  one  of  many 
instruments  used  to  determine  vibration-frequency. 

A  wavy  sound  caused  by  interference  of  sound  waves  is 
known  by  the  name  of  beats.  The  number  of  beats  per  second 
due  to  two  simple  tones  is  equal  to  the  difference  of  their 
respective  vibration-numbers.  Beats  are  one  of  the  chief  causes 
of  discord. 

XLIV.     VIBRATION  OF   STRINGS. 

The  vibration-frequency  of  strings  of  the  same  material  varies 
inversely  as  their  lengths  and  the  square  roots  of  their  weights, 
and  directly  as  the  square  roots  of  their  tension. 

XLV.     OVERTONES  AND   HARMONICS. 

Sounds  proceeding  from  instruments  vibrating  in  parts  are 
called  overtones.  If  the  vibration-number  of  the  overtone 
bears  some  simple  ratio  to  the  vibration-number  of  the  funda- 
mental, the  overtone  is  called  a  harmonic. 


434  SYLLABUS. 

Generally,  only  those  notes  harmonize  whose  fundamental 
tones  bear  to  one  another  ratios  expressed  by  small  numbers ; 
and  the  smaller  the  numbers  which  express  the  ratios  of  the 
rates  of  vibration,  the  more  perfect  is  the  harmony. 

XL VI.     QUALITY   IN  SOUND. 

Quality,  or  that  property  of  sound  which  enables  us  to  dis- 
tinguish different  sounds  having  the  same  pitch  and  intensity,  is 
shown  both  by  analysis  and  synthesis  to  depend  upon  what 
overtones  combine  with  its  fundamental,  and  on  their  relative 
intensities;  or,  briefly,  ^upon  the  form  of  vibration.  Sounds 
differ  only  in  intensity,  pitch,  and  quality.  The  manometric 
flame  apparatus  is  well  suited  to  illustrate  these  three  properties. 

XLVIII.     SOME    SOUND-RECEIVING   INSTRUMENTS. 

The  ear  is  a  mechanical  contrivance  for  the  transmission  of 
vibration  to  the  organs  of  sensation.  For  example,  the  aerial 
waves  cause  forced  vibrations  in  the  outer  membrane  or  tym- 
panum ;  these  are  communicated  by  a  chain  of  bones  to  the 
membranous  walls  of  the  vestibule,  and  thereby  to  the  liquid 
contained  in  the  cavity.  The  bristles  suspended  in  this  liquid 
take  up  and  analyze  the  vibrations,  much  as  when  we  sing  into 
a  piano  with  the  dampers  down,  only  those  strings  respond 
which  are  in  unison  with  the  sound  produced  'by  the  voice. 
The  bristles  stir  the  nerve  filaments  connected  with  them,  and 
the  nerve  transmits  to  the  brain  the  impressions  received. 

XLIX.     MUSICAL   INSTRUMENTS. 

In  pipes  the  vibration-frequency  varies  inversely  as  its 
length.  When  the  fundamental  of  an  open  pipe  is  sounded  its 
air-column  divides  itself  into  two  equal  vibrating  sections  with 
a  node  in  the  center,  hence  an  open  pipe  should  be  twice  as 
long  as  a  closed  pipe  to  produce  the  same  pitch. 


CHAPTER   VI. 

RADIANT   ENERGY. -LIGHT. 
L.   INTRODUCTION. 

That  we  receive  energy  from  the  sun,  and  that  nearly  all  the 
energy  employed  by  man  came  from  the  sun,  is  certain.  The 
average  amount  of  energy  received  by  the  earth  is  estimated  to 
be  83  ft.-lbs.  per  square  foot  of  surface  per  second  of  time 
(Daniell).  This  energy  appears  to  be  transmitted  in  the  form 
of  wave-motion.  This  method  of  transmission,  or  indeed  any 
method,  would  seem  to  require  a  medium  for  its  transmission. 
The  hypothetical  medium  has  received  the  name  of  ether,  and 
this  method  of  transmission  is  called  radiation.  Radiant 
energy  manifests  itself  as  heat,  light,  or  chemism  according  to 
the  object  upon  which  it  acts.  Light  is  the  vibration  of  ether 
that  may  be  appreciated  by  the  organ  of  sight. 

Luminous  bodies  are  seen  by  the  light  which  they  emit ; 
illuminated  bodies,  b}'  the  light  which  they  reflect.  Every  point 
of  a  luminous  body  emits  light  in  every  direction. 

The  intensity  of  light  diminishes  as  the  square  of  the  dis- 
tance from  the  source  increases.  (Why?) 

The  apparent  size  of  an  object  diminishes  as  its  distance 
from  the  eye  increases.  (Why?) 

The  velocity  with  which  light  traverses  interplanetary  space 
is  about  186,000  miles  per  second. 

LIH.   REFLECTION  OF  LIGHT. 

Light  is  so  reflected  that  the  angle  of  reflection  is  equal  to 
the  angle  of  incidence.  Owing  to  the  greater  or  less  roughness 
of  the  surfaces  of  all  objects  light  becomes  by  reflection  more  or 
less  scattered  or  diffused. 


186  SYLLABUS. 

The  amount  of  light  reflected  from  a  smooth  surface  in- 
creases rapidly  with  the  angle  of  incidence. 

Concave  mirrors  tend  to  produce  a  convergence  of  rays ; 
convex  mirrors  cause  divergence ;  plane  mirrors  do  not  alter 
the  relation  of  rays. 

Images  formed  by  plane  and  convex  mirrors  are  virtual 
images.  Images  formed  of  objects  situated  between  a  concave 
mirror  and  its  principal  focus  are  virtual ;  in  all  other  situations 
the  images  are  real. 

(Describe  the  variety  of  images  that  may  be  formed  by  a  con- 
cave mirror.  Describe  an  image  formed  by  a  convex  mirror ; 
also  one  formed  by  a  plane  mirror.) 


LIV.    REFRACTION. 

When  light  passes  obliquely  from  a  rarer  into  a  denser 
medium  it  is  refracted  toward  a  perpendicular  to  the  boundary 
plane  ;  if  from  a  denser  into  a  rarer  medium,  it  is  refracted 
from  the  perpendicular. 

The  ratio  of  the  sine  of  the  angle  of  incidence  to  the  sine  of 
the  angle  of  refraction  is  called  the  index  of  refraction,  and  is 
the  same  as  the  ratio  of  the  velocity  of  the  incident  to  that 
of  the  refracted  light. 

When  a  ray  passes  obliquely  from  a  vacuum  into  a  medium, 
the  index  of  refraction  is  greater  than  unity,  and  is  called  the 
absolute  index  of  refraction.  The  relative  index  of  refraction, 
from  any  medium  A,  into  another  B,  is  found  by  dividing  the 
absolute  index  of  B  by  the  absolute  index  of  A. 

When  the  angle  of  incidence  is  such  that  the  angle  of  refrac- 
tion is  90°,  i.e.,  the  reflected  ray  moves  in  the  plane  of  the 
refracting  surface,  the  angle  is  called  the  critical  angle.  Total 
reflection  occurs  when  rays  in  the  more  refractive  medium  aie 
incident  at  an  angle  greater  than  the  critical  angle. 


RADIANT   ENERGY.  —  LIGHT.  437 

LV.   LENSES 

£he  general  effect  of  convex  lenses  is  to  converge  trans 
rays  ;  and  of  concave  lenses,  to  cause  them  to  diverge. 
The  corresponding  linear  dimensions  of  an  object  and  its 
image  formed  by  a  convex  lens  are  to  one  another  as  the  re- 
spective distances  from  the  optical  center  of  the  lens. 

(Describe  the  variety  of  images  that  may  be  formed  by  convex 
concave  lenses.) 


LVI.     PRISMATIC   ANALYSIS   OF  LIGHT.  —  SPECTRA. 

When  a  beam  of  white  light  passes  through  an  optical  prism, 
tLa  colors  of  which  it  is  composed  are  separated  by  refraction, 
owing  to  their  different  degrees  of  refrangibility.  If  the  dif- 
ferent colors  are  again  brought  together,  white  light  is  repro- 
duced. 

Difference  of  color  is  a  difference  of  vibration-rate  or  wave- 
l"iigth.  In  a  dense  medium  the  shorter  waves  are  more 
retarded  than  the  longer  ones  ;  hence,  they  are  more  refracted. 
A  body  which  emits  white  light  sends  forth  simultaneously 
\\ftves  of  a  variety  of  lengths. 

Luminous  solids  and  liquids  give  continuous  spectra,  while 
gases  usually  give  discontinuous  or  bright-line  spectra.  Hence, 
tne  spectrum  reveals  the  state  of  the  substance  emitting  light. 

A  vapor  of  any  substance  is  opaque  to  those  rays  which  it 
vould  itself  emit  if  luminous.  Hence,  when  white  light 
traverses  vapors  capable  of  absorbing  certain  rays,  the  spectrum 
formed  by  the  transmitted  light  will  be  crossed  by  dark  lines. 
These  dark  lines  occur  where  bright  lines  would  be  formed  if 
the  same  vapors  were  rendered  luminous,  hence  the  former  are 
sometimes  called  reversed  spectra. 

No  two  substances  give  spectra  consisting  of  the  same  com- 
bination of  lines.  Spectrum  analysis  consists  in  determining 
the  presence  or  absence  of  given  substances  in  a  luminous 


438  SYLLABUS. 

vapor  by  the  presence  or  absence  of  their  characteristic  lines  in 
the  spectrum.  Likewise  the  substances  which  are  present  in 
the  solar  atmosphere  and  the  photosphere  can  be  determined  by 
the  reversed  lines  of  the  solar  spectrum. 

The  solar  spectrum  is  not  limited  in  either  direction  by  the 
visible  spectrum.  Although  the  eye  is  not  susceptible  to  impres- 
sions from  the  ultra-red  and  ultra-violet  rays,  yet  the  former 
are  quite  energetic  in  producing  heat,  and  the  latter  in  generat- 
ing chemical  action. 

LVil.    COLOR. 

Color  is  a  quality  of  the  light  which  illuminates,  and  not  of 
the  object  illuminated.  No  body  gives  color  to  light  which  it 
reflects  or  transmits. 

The  tendency  of  atmospheric  dust  is  to  absorb  the  colors  at 
the  violet  end  of  the  spectrum,  and  to  transmit  the  colors  at  the 
red  end.  On  the  other  hand,  it  tends  to  reflect  the  colors  of  the 
violet  end,  and  absorb  those  of  the  red.  Hence  the  redness  of 
the  light  at  sunrise  arid  sunset,  when  the  light  passes  long  dis- 
tances through  this  dust ;  also,  the  blueness  of  sky-light,  which 
is  reflected  light. 

Red,  green,  and  violet  are  thought  to  be  the  three  primary 
color-sensations,  and  all  other  colors  are  supposed  to  be  the 
product  of  mixed  sensations  of  these  three  in  varying  propor- 
tions. 

A  color  resulting  from  a  mixture  of  pigments  is  the  color 
that  is  left  after  the  two  pigments  have  absorbed  all  the  other 
colors,  and  is  not  the  result  of  a  combination  of  colors. 

When  any  two  colors  combined  will  produce  wrhite,  they  are 
said  to  be  complementary  to  each  other. 

Waves  of  light,  like  sound-waves,  may  interfere  so  as  to  pro- 
duce mutual  destruction.  If  the  light  is  monochromatic,  dark- 
ness is  the  result.  If  the  light  is  white,  and  only  waves  of 
certain  length  interfere,  then  a  color  is  produced  which  is  the 


RADIANT   ENERGY.  —  LIGHT.  439 

»-3Sult  of  the  subtraction  of  the  annihilated  color  from  white 
light.  Interference  may  be  caused  by  reflection  from  thin 
films,  and  by  the  bending  of  rays  of  light  around  the  edges  of 
opaque  objects. 

LVIII.    DOUBLE    REFRACTION  AND   POLARIZATION 
OF  LIGHT. 

Light  transmitted  through  the  crystals  of  certain  substances, 
notably  Iceland  spar,  suffers  a  double  refraction,  i.e.,  it  becomes 
divided,  and  pursues  two  different  paths. 

Ordinary  light  is  supposed  to  consist  of  vibrations  in  ether,  in 
every  possible  plane  at  right  angles  to  the  path  of  the  light. 
When,  by  reflection  or  transmission  through  certain  substances, 
it  is  reduced  to  vibrations  of  one  plane,  it  is  said  to  "be  polarized. 

LIX.    THERMAL   EFFECTS   OF   RADIATION. 

When  a  body  absorbs  largely  the  radiations  which  strike  it, 
i.e.,  when  the  undulations  of  the  ether  are  largely  transformed 
into  molecular  motion,  the  body  becomes  heated  thereby,  and  is 
said  to  be  athermanous.  But  if  the  nature  of  the  molecules  of 
a  body  is  such  that  their  motions  are  not  readily  quickened  by 
the  undulations,  but  the  body  allows  a  large  portion  of  the 
undulations  to  pass  through  it  unabsorbed,  then  is  it  slightly 
heated  thereby,  and  is  said  to  be  diatliermanous. 

All  bodies  emit  radiations,  and,  in  common  parlance,  are  said 
to  radiate  heat.  Good  absorbers  are  good  radiators ;  bad 
absorbers  are  bad  radiators.  The  absorbing  and  radiating 
power  of  a  body  of  the  same  substance  depends  largely  upon 
the  character  of  its  surface,  i.e.,  whether  it  be  bright  and 
smooth,  or  tarnished  and  rough.  Dew,  which  is  the  result  of 
condensation  of  the  watery  vapor  of  the  air,  collects  most  abun- 
dantly on  good  radiators,  inasmuch  as  the}7  part  with  their  heat 
rapidly,  and,  consequently,  become  cooler  than  poor  radiators. 


INDEX. 


[NUMBERS  REFEK  TO  PAGES.] 


Aberration,  Chromatic,  394. 

Spherical,  363. 
Absorption,  38,  30. 
Acceleration,  Unit  of,  128. 
Achromatic  lens,  395. 
Action  and  reaction,  116. 
Adhesion,  33. 
Air,  a  medium  of  wave-motion,  277. 

Weight  of,  3. 
Air-pump,  54. 
Air-waves,  282. 
Alphabet,  Telegraphic,  266. 
Amalgamating  zinc,  187. 
Ampere,  a  unit  of  current,  206. 
Ampere's  rule,  183;  theory,  218. 
Analysis  of  light,  364. 
Angles  of  incidence  and  reflection,  118. 
Antinodes,  276. 
Armature,  197. 
Artesian  wells,  70. 
Athermancy,  388. 
Atmosphere,  a  unit  of  pressure,  49. 
Attraction,  Phenomena  of,  20. 

mutual,  13,  20,  21. 


Ballistic  curve,  109. 

Barometer,  50. 

Battery,  Bunsen  or  Grove,  189. 

Gravity,  191. 

Grenet  or  bottle,  189. 

Smee,  188. 

Kind  of  to  use,  405. 

Qualities  of  good,  210. 
Batteries,  Arrangement  of,  207. 

Thermo,  235. 

Various,  188. 
Beam  of  light,  328. 
Beats,  302. 


Bells,  323. 

Blake  transmitter,  271. 
Boiling,  Laws  of,  101. 
Brittleness,  31. 
Buoyant  force  of  fluids,  78. 

C. 

Camera  Obscura,  392. 

Photographer's,  392. 
Candle-power,  334. 
Capillarity,  34. 

Celestial  chemistry  and  physics,  372 
Center  of  gravity,  96. 
Centrifugal  force,  102. 
Centripetal  force,  102. 
C.G.S.  system,  125. 
Chemical  changes,  9. 
Cohesion,  23. 
Coil,  Rhumkorff's,  233. 
Coils,  Induction,  232. 
Cold,  Method*  of  producing,  167 
Color  by  absorption,  374. 

by  interference,  379. 

by  polarization,  387. 

Cause  of,  367. 

Effect  of  contrast  of,  379. 
Colors,  Complementary,  379. 

Mixing,  376. 

Primary,  365. 

Sky,  375. 

Compound  substances,  8. 
Compressibility  of  gases,  52. 
Condenser,  249. 
Conservation  of  energy,  174. 
Constitution  of  matter,  6. 
Correlation  of  energy,  174. 
Couple,  Mechanical,  95. 
Critical  angle,  354. 
Current  attraction,  216. 

Extra,  261. 


INDEX. 


Current  induction,  230. 

Strength  of,  197,  201. 
Currents,  Earth,  224. 

Laws  of,  215,  217. 
Curvilinear  motion,  101. 
Cutting  glass,  401. 

D. 

Density,  7,  79. 
l>ew,  391. 

point,  164. 
Dialysis,  40. 
Diamagnetism,  225. 
Diathermancy,  388. 
Diffraction,  381. 
Diffusion,  39. 
Discharge,  Electrical,  242. 
Discord,  Cause  of,  307. 
Dispersion  of  light,  365. 
Distillation,  162. 
Ductility,  32. 
Dynamics  defined,  44. 

of  fluids,  44. 

Dynamo  machines,  227. 
Dyne,  125,  128. 

E. 
Ear,  315. 

Earth,  a  magnet,  220,  223. 
Elasticity,  29. 
Electric  candle,  260. 

lamp,  260. 

light,  259. 
Electrical  attractions,  etc.,  238,  252. 

machines,  245. 

measurements,  197. 
Electricity,  Chemical  effect  of,  19'2. 

Current,  179. 

Prictional,  237. 

Heating  effect  of,  191. 

how  it  originates,  184. 

Luminous  effect  of,  192,  253. 

Magnetic  effect  of,  196. 

Physiological  effect  of,  195. 

Thermo,  234. 

Two  states  of,  238. 

Useful  applications  of,  258. 

What  is,  257. 
Electrification,  237. 

on  surface,  244. 

Two  kinds  of,  239. 


Electro-chemical  series,  186. 
Electrodes,  183. 
Electrolysis,  193. 
Electro-magnet,  196. 

Electro-magnetic  machines,  262. 
Electro-motive  force,  204. 
Electrophorus,  246. 
Electroplating,  262. 
Electroscope,  237. 
Electro  typing,  261. 
Energy,  Conservation  of,  174. 

contrasted  with  momentum,  123, 

Correlation  of,  174. 

defined,  121. 

Formula  for,  124. 

Potential  and  kinetic,  121. 

Radiant,  327. 

Transformation  of,  128,  129,  2576 

Unit  of,  123. 
Engine,  Steam,  175. 
Engines,  Kinds  of  steam,  177. 
Equilibrant  force,  95. 
Equilibrium,  44. 

Three  states  of,  98. 
Erg,  126,  128. 

Ether,  a  medium  of  motion,  326. 
Evaporation,  163. 
Expansibility  of  gases,  52. 
Expansion,  Abnormal,  150. 

by  heat,  148. 

Coefficients  of,  149. 

Power  of,  150. 
Experiment  defined,  1. 
Eye,  Human,  393. 

F. 

Falling  bodies,  104. 
Fire-alarm,  Electric,  267, 
Flexibility,  29. 

Foci,  Conjugate,  360. 
Focus,  Principal,  346,  359. 

Virtual,  360. 
Foot-pound,  120. 
Force,  Absolute  unit  of,  125. 

Centrifugal,  102. 

Centripetal,  102. 

defined,  12,  13. 

Equilibrant,  95. 

Gravity  unit  of,  126. 

Measure  of  a,  124. 


INDEX. 


Force,  Measure  of  the  effect  of,  126. 

Resultant,  91. 
Forces,  Composition  of,  91,  94,  95. 

Graphic  representation  of,  90. 

Molar,  13. 

Molecular,  13. 

Resolution  of,  92. 
Fraunhofer's  lines,  372. 
Fusion,  Laws  of,  161. 

G. 

Galvanometer,  198,  404. 

Tangent,  199. 
Galvanoscope,  184. 
Gaseous  bodies,  Laws  of,  156. 
Gases,  Kinetic  theory  of,  157. 
Gravitation,  14,  20. 
Gravity,  Acceleration  of,  106. 

Center  of,  96. 

Force  of,  14,  21. 

H. 

Hardness,  28. 
Harmonics,  305. 
Harmony,  Cause  of,  307. 
Hearing,  Limits  of,  301. 
Heat,  Capacity  for,  171. 

Conduction  of,  142. 

Convection  of,  143. 

convertible,  138,  165. 

defined,  139. 

Diffusion  of,  142. 

Expansion  by,  148. 

from  chemical  action,  140. 

Mechanical  equivalent  of,  17.">. 

Origin  of  animal,  140. 

Reference  tables  for  specific,  172. 

Home  sources  of,  138. 

Specific,  170. 

units,  165. 
Helix,  196. 
Horse-power,  121. 
Hydrogen  at  the  copper  plate,  185. 
Hydrometers,  83. 
Hydrostatic  bellows,  64. 

press,  64. 

I. 

Images,  After,  379. 
Formation  of,  346,  360. 


Images,  Real,  347. 

through  apertures,  330. 

To  construct,  347,  361. 

Virtual,  342,  362. 
Impenetrability,  1,  6. 
Induction,  241. 

'coils,  232. 
Inertia,  90. 
Interference  of  light,  379. 

of  sound-waves,  274,  322. 
Insulation,  243. 

J. 

Joule's  equivalent,  175. 


Kilogrammeter,  120. 
Kinetic  energy,  121. 
theory  of  gases,  157. 


Law,  Mariotte's,  156. 

of  Charles,  156. 
Laws  of  fusion  and  boiling,  161. 

of  gaseous  bodies,  156. 
Lenses,  357. 

Effects  of,  358. 
Leyden  jar,  250. 
Light,  a  form  of  energy,  325., 

Analysis  of,  364. 

Diffused,  340. 

Electric,  259. 

invisible,  327. 

Reflection  of,  339. 

Synthesis  of,  366. 
Lightning,  255. 

rods,  255. 

Liquid  surface  level,  69. 
Luminous  and  illuminated  bodies,  329. 

M. 

Machines,  131. 

Law  of,  133. 

Uses  of,  132. 
Magnets  and  magnetism,  212,  224. 

Law  of,  213. 

Natural,  223. 

not  sources  of  energy,  225. 
Magnetic  transparency,  213. 


INDEX. 


Magnetism,  Cause  of  the  earth's,  223. 
Magneto  machines,  227. 

electric  induction,  226. 
Malleability,  32. 
Manometric  flames,  312. 
Mariotte's  law,  57, 156. 
Mass,  7,  20. 
Matter  a  constant  quantity,  10,  11. 

Conditions  of,  24. 

Crystalline  and  amorphous,  24. 

Three  states  of,  15. 
Metric  system,  399. 
Microphone,  270. 
Microscope,  Simple,  362. 

Compound,  391. 

Minuteness  of  particles  of  matter,  3. 
Mirrors,  Reflection  from,  341. 
Molecule,  4. 
Momentum,  115. 
Motion,  Accelerated,  104. 

Curvilinear,  101. 

First  law  of,  89. 

Formulas  for  uniformly  accelerated, 
106. 

Kinds  of,  87. 

Retarded,  107. 

Second  law  of,  91. 

Third  law  of,  117. 

versus  rest,  86,  87. 
Multiple  reflection,  343. 
Musical  instruments,  319. 

Scale,  300. 


Nodes,  275. 
Noise,  297. 


N. 


O. 


Ohm,  202. 
Ohm's  law,  205. 
Opacity,  328. 

Oscillation,  Center  of,  111. 
Osmose,  40. 
Overtones,  305. 


Parabolic  curve,  109. 
Paramagnetism,  225. 
Pencil  of  light,  328. 
Pendulum,  110. 


Pendulum,  Center  of  oscillation  of,  111, 

Center  of  percussion  of,  113. 
Phenomenon,  1. 
Phonograph,  317. 
Photometry,  333. 
Physical  changes,  9. 
Physics  defined,  129. 
Pigments,  375. 

Mixing,  378. 
Pitch,  298. 

Points,  Effects  of,  252. 
Polarity.  28,  214. 
Polariscope,  387. 
Polarization.  384. 

of  plates,  188. 
Poles  of  hattery,  183. 
Porosity,  7. 
Potential,  Electric,  183,  244. 

energy,  121,  168. 
Porte  lumiere,  339,  407. 
Press,  Hydrostatic,  64. 
Pressure  in  fluids,  44-79. 
Primary  colors,  365. 
Prisms,  Optical,  357. 
Projectiles,  108. 
Pump,  Air,  54-57. 

Force,  75- 

Lifting,  74,  75. 

Q. 

Quality  of  sound-  300. 
Qualities  of  perfect  battery.  21^ 

R. 

Radiation,  327. 

Thermal  effects  of,  388. 
Radiator,  327. 
Radiometer,  325. 
Random  of  projectiles,  108 
Ray,  328. 
Reaction,  116. 
Reflection,  Angle  of,  118. 

Law  of,  118. 

Multiple,  343. 

Total,  355. 
Refraction,  350. 

Cause  of,  351. 

Double,  383. 

Index  of,  352. 


INDEX. 


Relay  and  repeater,  264. 
Repulsion  mutual,  13. 
Resonance,  290. 
Resonators,  291. 
Resistance,  Formula  for,  202. 

Internal,  203. 

External,  204. 
Rest,  86,  87. 
Resultant  force,  91. 


Shadows,  331. 
Simple  substances,  8. 
Siphon,  72. 
Siren,  299. 

Solution  of  solids,  37. 
Sonometer,  303. 
Sound,  Analysis  of,  309. 

how  it  originates,  280. 

how  it  travels,  281. 

Loudness  of,  288. 

media,  283. 

Musical,  297. 

Pitch  of,  298. 

Quality  of,  309. 

Reinforcement  of,  290. 

Reflection  of,  285. 

Refraction  of,  287. 

Synthesis  of,  310. 

Velocity  of,  284. 

what  it  is,  283. 
Sounder,  264. 
Sounding  air-columns,  319. 

plates,  321. 

Sound-waves,  272,  274,  280. 
Speaking  tubes,  289. 
Specific  gravity,  80. 
Spectra,  Bright-line,  369. 

Continuous,  368. 

Dark-line,  370. 

Heat  and  chemical,  373. 
Spectrum  analysis,  371. 

Solar,  365. 

Spectroscope,  368. 
Stability  of  bodies,  99. 
Steam  engine,  175. 
Stereopticon,  395. 
Summary  of  elec.  measurements,  208. 

of  mechanical  units  and  formulas,  127. 
Sun  as  a  source  of  energy,  141. 


T. 

Table  of  boiling  points,  161. 

of  E.M.F.,  205. 

of  indices  of  refraction.  353. 

of  melting  points,  161. 

of  metric  system,  399. 

of  natural  tangents,  403. 

of  specific  gravities,  402. 

of  specific  heat,  172. 
Telegraph,  263. 

Fac-simile,  266. 
Telegraphic  alphabet.  266. 
Telephone,  Bell,  269,  318. 
Telephone,  Dolbear,  271. 

String,  318. 

Telescope,  Astronomical,  392. 
Temperature,  Absolute,  155. 

defined,  141. 

measured  by  expansion,  151. 
Tenacity,  32. 
Tension,  44. 

Theory  of  exchanges,  390. 
Thermo  batteries,  235. 
Thermopile,  236. 
Thermo-dynamics,  174. 
Thermometer,  Air,  154. 

Construction  of,  151. 

Graduation  of,  152. 
Thermometry,  151. 
Transformation  of  energy,  128,  129, 

257. 

Translucency,  328. 
Transparency,  328. 
Tubes,  Speaking,  289. 


TJ. 

Vndulatory  theory,  327. 


V. 

Vacuum,  Absolute,  56. 
Variation  of  needle,  222. 
Velocity,  Accelerated,  104. 

defined,  87. 

of  electric  discharge,  254. 

of  light,  337. 

of  sound,  284,  292. 

Unit  of,  128. 
Ventilation,  146. 


INDEX. 


Ventral  segment,  276. 
Vibration,  Direction  of,  273. 

of  strings,  303. 

Propagation  of,  274. 

Sound,  272. 
Vibrations,  Complex,  273,  305. 

Composition  of,  311. 

Forced,  295. 

Stationary,  275. 

Sympathetic,  295. 
Viscosity,  31. 
Visual  angle,  335. 
Vocal  organs,  323. 
Volt,  205. 
Voltaic  arc,  259. 
Voltameter,  198. 


W. 

Waves,  Air,  282. 

Interference  of,  274,  294. 

Longitudinal,  276. 

Reflection  of,  274. 

Sound,  272,  274,  280. 

Water,  276. 
Wave-length,  274,  292. 

Measuring,  292. 
Wave-lengths  of  light,  367. 
Wave-line,  274,  279. 
Wave  -  motion,  Apparatus    to    illue 

trate,  406. 

Wave-propagation,  278. 
Weber,  206. 


APPARATUS  ADAPTED  TO  GAGE'S  PHYSICS. 


Immediately  following  the  first  appearance  of  the  book,  in  Novem- 
ber, 1882,  the  Publishers  received  many  calls  for  apparatus  especially 
adapted  to  the  carrying  out  of  the  plan  of  the  book.  It  appearing 
almost  a  necessity,  Mr.  Gage  reluctantly  consented  to  give  some  atten- 
tion to  the  furnishing  of  schools  with  cheap  and  efficient  apparatus, 
thereby  rendering  it  possible  for  every  school  in  the  land,  however 
limited  its  means,  to  teach  this  branch  in  a  rational  manner.  In 
future,  he  will  devote  a  portion  of  his  time  to  the  study  of  (1)  new 
forms  of  apparatus,  and  (2)  methods  of  making  the  same  pieces,  with 
slight  modifications,  answer  a  variety  of  purposes.  His  popular 
"little  marvels,"  the  New  Porte-Lumiere,  Seven  iti  One  Apparatus. 
Eight  in  One  Apparatus,  improved  Pascal's  Vases,  Bunsen  Batteries, 
Apparatus  for  making  electrical  measurements,  etc.,  are  a  sufficient 
testimony  to  his  success  thus  far. 

Only  a  minimum  profit  is  charged  on  this  apparatus,  so  that  no 
discounts  are  possible,  and  the  school  which  has  but  a  dollar  to  expend 
can  purchase  on  terms  which  will  compare  favorably  with  the  lowest 
net  prices  ever  offered.  A  set  of  this  apparatus  will  be  kept  on  con- 
stant exhibition  at  our  office,  13  Tremont  Place,  Boston. 

For  price  lists,  and  other  information  respecting  the  apparatus, 
address 

A.  P.  GAGE,  English  High  School,  Boston,  Mass, 

Unsolicited  testimonial  front  L.  B.  Charbonnier,  Professor  of  Physics  in  the 

University  of  Georgia. 

The  apparatus  ordered  from  you  has  been  received  to-day.  Like  all  previ- 
ously bought  from  you,  it  gives  entire  satisfaction.  You  are  really  doing  an 
excellent  work  for  our  schools  in  furnishing  such  apparatus  as  you  do,  and  at 
the  most  reasonable  cost.  I  have  had  excellent  opportunity  to  judge  of  the 
quality  of  your  work,  as  I  have  under  my  charge  an  extensive  collection  of 
apparatus  bought  from  different  makers  here  and  in  Europe.  The  apparatus 
bought  of  you  is  used  by  the  students  of  the  lower  class  in  the  laboratory ; 
and  hence  I  have  been  able  to  compare  your  work  with  that  of  other  makers. 
I  feel  it  due  you  to  testify  to  the  excellence  of  your  work.  There  is  no  reason 
why  physical  science  should  not  be  now  fully  illustrated  in  our  schools,  when 
the  inexpensiveness  of  your  apparatus  brings  it  within  the  reach  of  the  most 
moderate  means. 

ATHENS,  GA.,  October  13,  1887. 


GINN  &  COMPANY,  Publishers,  Boston,  New  York,  and  Chicago. 


86  PHYSICAL   SCIENCE. 

Introduction  to  Physical  Science. 

By  A.  P.  GAGE,  Instructor  in  Physics  in  the  English  High  School,  Bos- 
ton, Mass.,  and  Author  of  Elements  of  Physics,  etc.  12mo.  Cloth, 
viii  +  353  pages.  With  a  chart  of  colors  and  spectra.  Mailing  Price, 
$1.10  ;  for  introduction,  $1.00  ;  allowance  for  an  old  book  in  exchange, 
30  cents. 

HIRE  great  and  constantly  increasing  popularity  of  Gage's  Ele- 
ments of  Physics  has  created  a  demand '  for  an  equally  good 
but  easier  book,  on  the  same  plan,  suitable  for  schools  that  can 
give  but  a  limited  time  to  the  study.  The  Introduction  to  Physical 
Science  has  been  prepared  to  supply  this  demand. 

Accuracy  is  the  prime  requisite  in  scientific  text-books.  A 
false  statement  is  not  less  false  because  it  is  plausible,  nor  an  in- 
conclusive experiment  more  satisfactory  because  it  is  diverting. 
In  books  of  entertainment,  such  things  may  be  permissible ;  but 
in  a  text-book,  the  first  essentials  are  correctness  and  accuracy. 
It  is  believed  that  the  Introduction  will  stand  the  closest  expert 
scrutiny.  Especial  care  has  been  taken  to  restrict  the  use  of  scien- 
tific terms,  such  as  force,  energy,  power,  etc.,  to  their  proper  signifi- 
cations. Terms  like  sound,  light,  color,  etc.,  which  have  commonly 
been  applied  to  both  the  effect  and  the  agent  producing  the  effect 
have  been  rescued  from  this  ambiguity. 

Recent  Advances  in  physics  have  been  faithfully  recorded, 
and  the  relative  practical  importance  of  the  various  topics  has  been 
taken  into  account.  Among  the  new  features  are  a  full  treatment 
of  electric  lighting,  and  descriptions  of  storage  batteries,  methods 
of  transmitting  electric  energy,  simple  and  easy  methods  of  making 
electrical  measurements  with  inexpensive  apparatus,  the  compound 
steam-engine,  etc.  Static  electricity,  which  is  now  generally  re- 
garded as  of  comparatively  little  importance,  is  treated  briefly; 
while  dynamic  electricity,  the  most  potent  and  promising  physical 
element  of  our  modern  civilization,  is  placed  in  the  clearest  light 
of  our  present  knowledge. 

In  Interest  and  Availability  the  Introduction  will,  it  is 
believed,  be  found  no  less  satisfactory.  The  wide  use.  of  the 
Elements  under  the  most  varied  conditions,  and,  in  particular, 
the  author's  own  experience  in  teaching  it,  have  shown  how  to 
improve  where  improvement  was  possible.  The  style  will  be  found 


PHYSICAL   SCIENCE. 


87 


suited  to  the  grades  that  will  use  the  book.  The  experiments  are 
varied,  interesting,  clear,  and  of  practical  significance,  as  well  as 
simple  in  manipulation  and  ample  in  number.  Certain  subjects, 
that  are  justly  considered  difficult  and  obscure  have  been  omitted ; 
as,  for  instance,  certain  laws  relating  to  the  pressure  of  gases  and 
the  polarization  of  light.  The  Introduction  is  even  more  fully 
illustrated  than  the  Elements. 

In  General.  The  Introduction,  like  the  Elements,  has  this  distinct 
and  distinctive  aim,  —  to  elucidate  science,  instead  of  "populariz- 
ing "  it ;  to  make  it  liked  for  its  own  sake,  rather  than  for  its  gilding 
and  coating ;  and,  while  teaching  the  facts,  to  impart  the  spirit  of 
science,  —  that  is  to  say,  the  spirit  of  our  civilization  and  progress. 


George  E.  Gay,  Prin.  of  High 
School,  Maiden,  Mass.:  With  the 
matter,  both  the  topics  and  their  pre- 
sentation, I  am  better  pleased  than 
with  any  other  Physics  I  have  seen. 

E.  H.  Perkins,  Supt.  of  Schools, 
Chicopee,  Mass. :  I  have  no  doubt 
we  can  adopt  it  as  early  as  next 
month,  and  use  the  same  to  great  ad- 
vantage in  our  schools.  (Feb.  6, 1888.) 

Mary  E.  Hill,  Teacher  of  Physics, 
Northfield  Seminary,  Mass.:  I  like 
the  truly  scientific  method  and  the 
clearness  with  which  the  subject  is 
presented.  It  seems  to  me  admirably 
adapted  to  the  grade  of  work  for 
which  it  is  designed.  (Mar.  5,  '88.) 

JohnPickard,  Prin.  of  Portsmouth 
High  School,  N.H. :  I  like  it  exceed- 
ingly. It  is  clear,  straightforward, 
practical,  and  not  too  heavy. 

Ezra  Brainerd,  Pres.  and  Prof, 
of  Physics,  Middlebitry  College,  Vt.: 
I  have  looked  it  over  carefully,  and 
regard  it  as  a  much  better  book  for 
high  schools  than  the  former  work. 
(Feb.  6,  1888.) 

James  A.  De  Boer,  Prin.  of  High 
School,  Montpelier,  Vt. :  I  have  not 
only  examined,  but  studied  it,  and 
consider  it  superior  as  a  text-book  to 
auy  other  I  have  seen.  (Feb.  10,  '88.) 


E.  B.  Eosa,  Teacher  of  Physics, 
English  and  Classical  School,  Provi- 
dence, R.I. :  I  think  it  the  best  thing 
in  that  grade  published,  and  intend 
to  use  it  another  year.  (Feb.  23,  '88.) 

G.  H.  Patterson,  Prin.  and  Prof,  of 
Physics,  Berkeley  Sch.,  Providence, 
R.I.:  A  very  practical  book  by  a 
practical  teacher.  (Feb.  2,  1888.) 

George  E.  Beers,  Prin.  of  Evening 
High  School,  Bridgeport,  Conn.  : 
The  more  I  see  of  Professor  Gage's 
books,  the  better  I  like  them.  They 
are  popular,  and  at  the  same  time 
scientific,  plain  and  simple,  full  and 
complete.  (Feb.  18,  1888.) 

Arthur  B.  Chaff ee,  Prof,  in  Frank- 
lin College,  Ind. :  I  am  very  much 
pleaised  with  the  new  book.  It  will 
suit  the  average  class  better  than  the 
old  edition. 

W.  D.  Kerlin,  Supt.  of  Public 
Schools,  New  Castle,  Ind.:  I  find 
that  it  is  the  best  adapted  to  the 
work  which  we  wish  to  do  in  our 
high  school  of  any  book  brought  to 
my  notice. 

C.  A.  Bryant,  Supt.  of  Schools, 
Paris,  Tex. :  It  is  just  the  book  for 
high  schoolc.  I  shall  use  it  next 
year. 


88  PHYSICAL   SCIENCE. 

Introduction  to  Chemical  Science. 


By  R.  P.  WILLIAMS,  Instructor  in  Chemistry  in  the  English  High 
School,  Boston.  12mo.  Cloth.  210  pages.  Mailing  Price,  90  cents;  for 
introduction,  80  cents;  Allowance  for  old  book  in  exchange,  25  cents. 

TN    a  word,  this  is  a  working  chemistry  —  brief  but  adequate. 
Attention  is  invited  to  a  few  special  features  :  — 

1.  This  book  is  characterized  by  directness  of  treatment,  by  the 
selection,  so  far  as  possible,  of  the  most  interesting  and  practical 
matter,  and  by  the  omission  of  what  is  unessential. 

2.  Great  care  has  been   exercised   to   combine   clearness  with 
accuracy  of  statement,  both  of  theories  and  of  facts,  arid  to  make 
the  explanations  both  lucid  and  concise. 

3.  The   three   great   classes    of    chemical    compounds  —  acids, 
bases,  and  salts  —  are  given  more  than  usual  prominence,  and  the 
arrangement  and  treatment  of  the  subject-matter  relating  to  them 
is  believed  to  be  a  feature  of  special  merit. 

4.  The  most  important  experiments  and  those  best  illustrating 
the  subjects  to  which  they  relate,  have  been  selected  ;  but  the  modes 
of  experimentation  are  so  simple  that  most  of  them  can  be  per- 
formed by  the  average  pupil  without  assistance  from  the  teacher. 

5.  The  necessary  apparatus  and  chemicals  are  less  expensive 
than  those  required  for  any  other  text-book  equally  comprehensive. 

6.  The  special  inductive  feature  of  the  work  consists  in  call- 
ing attention,  by  query  and   suggestion,  to  the  most   important 
phenomena  and  inferences.     This  plan  is  consistently  adhered  to. 

7.  Though  the  method  is  an  advanced  one,  it  has  been  so  sim- 
plified that  pupils  experience  no  difficulty,  but  rather  an  added 
interest,    in   following  it ;    the   author   himself    has    successfully 
employed  it  in  classes  so  large  that  the  simplest  and  most  practical 
plan  has  been  a  necessity. 

8.  The  book  is  thought  to  be  comprehensive  enough  for  high 
schools  and  academies,  and  for  a  preparatory  course  in  colleges  and 
professional  schools. 

9.  Those  teachers  in  particular  who  have  little  time  to  prepare 
experiments  for  pupils,  or  whose  experience  in  the  laboratory  has 
been  limited,  will  find  the  simplicity  of  treatment  and  of  experi- 
mentation well  worth  their  careful  consideration. 

For  testimonials,  see  the  special  circular. 


VB  35990 


541.788 


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